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Title: The hitchhiker's guide to 4d $$\mathcal{N}=2$$ superconformal field theories

Abstract

Superconformal field theory with \mathcal{N}=2 𝒩 = 2 supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over non-perturbative effects, yet the theory is still flexible enough to incorporate a large landscape of quantum systems. Here we aim to offer a guidebook to fundamental features of the 4d \mathcal{N}=2 𝒩 = 2 superconformal field theories and basic tools to construct them in string/M-/F-theory. The content is based on a series of lectures at the Quantum Field Theories and Geometry School in July 2020.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [7]
  1. Swansea University
  2. Institute of Space Sciences and Technologies of Asturias, University of Oviedo
  3. University of Hamburg, Institute for Theoretical Physics
  4. The University of Texas at Austin
  5. University of California, San Diego
  6. Harvard University, New York University
  7. Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Heidelberg University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1894736
Grant/Contract Number:  
SC0009919
Resource Type:
Published Article
Journal Name:
SciPost Physics Lecture Notes
Additional Journal Information:
Journal Name: SciPost Physics Lecture Notes; Journal ID: ISSN 2590-1990
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Akhond, Mohammad, Arias Tamargo, Guillermo, Mininno, Alessandro, Sun, Hao-Yu, Sun, Zhengdi, Wang, Yifan, and Xu, Fengjun. The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories. Netherlands: N. p., 2022. Web. doi:10.21468/SciPostPhysLectNotes.64.
Akhond, Mohammad, Arias Tamargo, Guillermo, Mininno, Alessandro, Sun, Hao-Yu, Sun, Zhengdi, Wang, Yifan, & Xu, Fengjun. The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories. Netherlands. https://doi.org/10.21468/SciPostPhysLectNotes.64
Akhond, Mohammad, Arias Tamargo, Guillermo, Mininno, Alessandro, Sun, Hao-Yu, Sun, Zhengdi, Wang, Yifan, and Xu, Fengjun. Wed . "The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories". Netherlands. https://doi.org/10.21468/SciPostPhysLectNotes.64.
@article{osti_1894736,
title = {The hitchhiker's guide to 4d $\mathcal{N}=2$ superconformal field theories},
author = {Akhond, Mohammad and Arias Tamargo, Guillermo and Mininno, Alessandro and Sun, Hao-Yu and Sun, Zhengdi and Wang, Yifan and Xu, Fengjun},
abstractNote = {Superconformal field theory with \mathcal{N}=2 𝒩 = 2 supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over non-perturbative effects, yet the theory is still flexible enough to incorporate a large landscape of quantum systems. Here we aim to offer a guidebook to fundamental features of the 4d \mathcal{N}=2 𝒩 = 2 superconformal field theories and basic tools to construct them in string/M-/F-theory. The content is based on a series of lectures at the Quantum Field Theories and Geometry School in July 2020.},
doi = {10.21468/SciPostPhysLectNotes.64},
journal = {SciPost Physics Lecture Notes},
number = ,
volume = ,
place = {Netherlands},
year = {Wed Oct 26 00:00:00 EDT 2022},
month = {Wed Oct 26 00:00:00 EDT 2022}
}

Works referenced in this record:

N = 2 dualities
journal, August 2012


Geometric engineering, mirror symmetry and 6 d 1 0 → 4 d N = 2 $$ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $$
journal, November 2015

  • Del Zotto, Michele; Vafa, Cumrun; Xie, Dan
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)123

The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap
journal, March 2016

  • Beem, Christopher; Lemos, Madalena; Liendo, Pedro
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)183

Superconformal fixed points with En global symmetry
journal, March 1997


Phases of N = 1 supersymmetric gauge theories in four dimensions
journal, December 1994


Holographic Duals of Argyres-Douglas Theories
journal, November 2021


Operator product expansions in four-dimensional superconformal field theories
journal, December 1996


Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus
journal, December 1983


Seiberg–Witten Differential via Primitive Forms
journal, March 2019


Infinitely many $ \mathcal{N} $ = 2 SCFT with ADE flavor symmetry
journal, January 2013

  • Cecotti, Sergio; Del Zotto, Michele
  • Journal of High Energy Physics, Vol. 2013, Issue 1
  • DOI: 10.1007/JHEP01(2013)191

Schur indices, BPS particles, and Argyres-Douglas theories
journal, January 2016


$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009


Liberating confinement from Lagrangians: 1-form symmetries and lines in 4d N=1 from 6d N=(2,0)
journal, January 2022


Three-loop results in two-loop finite supersymmetric gauge theories
journal, January 1985


Coulomb and Higgs branches from canonical singularities. Part 0
journal, February 2021

  • Closset, Cyril; Schäfer-Nameki, Sakura; Wang, Yi-Nan
  • Journal of High Energy Physics, Vol. 2021, Issue 2
  • DOI: 10.1007/JHEP02(2021)003

Magnetic quivers for rank 2 theories
journal, March 2022

  • Bourget, Antoine; Grimminger, Julius F.; Martone, Mario
  • Journal of High Energy Physics, Vol. 2022, Issue 3
  • DOI: 10.1007/JHEP03(2022)208

N=2 superconformal models, Landau-Ginsburg hamiltonians and the ϵ expansion
journal, June 1989


Chiral Green's functions in superconformal field theory
journal, March 2000


An exact relation for the Gell-Mann-Low function in supersymmetric electrodynamics
journal, January 1986


Electric-magnetic duality and the geometric Langlands program
journal, January 2007


Explicit supersymmetry breaking can preserve finiteness in rigid N=2 supersymmetric theories
journal, August 1983


An SU(2) anomaly
journal, November 1982


4d $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras
journal, April 2021


More on $$ \mathcal{N} $$ =2 S-folds
journal, January 2021

  • Giacomelli, Simone; Martone, Mario; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2021, Issue 1
  • DOI: 10.1007/JHEP01(2021)054

Bootstrapping Coulomb and Higgs branch operators
journal, January 2021

  • Gimenez-Grau, Aleix; Liendo, Pedro
  • Journal of High Energy Physics, Vol. 2021, Issue 1
  • DOI: 10.1007/JHEP01(2021)175

Superconformal partition functions and non-perturbative topological strings
journal, October 2018

  • Lockhart, Guglielmo; Vafa, Cumrun
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)051

Topological Disorder Operators in Three-Dimensional Conformal Field Theory
journal, November 2002


Multiplets of superconformal symmetry in diverse dimensions
journal, March 2019

  • Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
  • Journal of High Energy Physics, Vol. 2019, Issue 3
  • DOI: 10.1007/JHEP03(2019)163

Magnetic quivers and line defects — On a duality between 3d $$ \mathcal{N} $$ = 4 unitary and orthosymplectic quivers
journal, February 2022

  • Nawata, Satoshi; Sperling, Marcus; Wang, Hao Ellery
  • Journal of High Energy Physics, Vol. 2022, Issue 2
  • DOI: 10.1007/JHEP02(2022)174

Conformal invariance in N = 4 supersymmetric Yang-Mills theory
journal, April 1981


On 4d rank-one N = 3 $$ \mathcal{N}=3 $$ superconformal field theories
journal, September 2016

  • Nishinaka, Takahiro; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)116

Solution of N = 2 gauge theories via compactification to three dimensions
journal, November 1998


Tinkertoys for the E7 theory
journal, May 2018

  • Chacaltana, Oscar; Distler, Jacques; Trimm, Anderson
  • Journal of High Energy Physics, Vol. 2018, Issue 5
  • DOI: 10.1007/JHEP05(2018)031

Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions
journal, April 2022

  • Closset, Cyril; Schäfer-Nameki, Sakura; Wang, Yi-Nan
  • Journal of High Energy Physics, Vol. 2022, Issue 4
  • DOI: 10.1007/JHEP04(2022)061

On orientifolds, discrete torsion, branes and M theory
journal, June 2000


Tinkertoys for the D N series
journal, February 2013

  • Chacaltana, Oscar; Distler, Jacques
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)110

The ABCDEFG of instantons and W-algebras
journal, March 2012

  • Keller, Christoph A.; Mekareeya, Noppadol; Song, Jaewon
  • Journal of High Energy Physics, Vol. 2012, Issue 3
  • DOI: 10.1007/JHEP03(2012)045

Evidence for F-theory
journal, June 1996


Compactifications of F-theory on Calabi-Yau threefolds. (I)
journal, August 1996


Argyres-Douglas theories in class S without irregularity
journal, May 2022


Instanton sums and five-dimensional gauge theories
journal, March 1998


On holomorphic dependence and infrared effects in supersymmetric gauge theories
journal, August 1991


Liouville Correlation Functions from Four-Dimensional Gauge Theories
journal, January 2010

  • Alday, Luis F.; Gaiotto, Davide; Tachikawa, Yuji
  • Letters in Mathematical Physics, Vol. 91, Issue 2
  • DOI: 10.1007/s11005-010-0369-5

Lagrangians for generalized Argyres-Douglas theories
journal, October 2017

  • Benvenuti, Sergio; Giacomelli, Simone
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)106

Quiver origami: discrete gauging and folding
journal, January 2021

  • Bourget, Antoine; Hanany, Amihay; Miketa, Dominik
  • Journal of High Energy Physics, Vol. 2021, Issue 1
  • DOI: 10.1007/JHEP01(2021)086

4d $\mathcal{N}=2$ SCFT and singularity theory Part III: Rigid singularity
journal, January 2018

  • Chen, Bingyi; Xie, Dan; Yau, Stephen S. -T.
  • Advances in Theoretical and Mathematical Physics, Vol. 22, Issue 8
  • DOI: 10.4310/ATMP.2018.v22.n8.a2

S-folds and 4d N $$ \mathcal{N} $$ = 3 superconformal field theories
journal, June 2016


Exceptional N = 3 $$ \mathcal{N}=3 $$ theories
journal, December 2017

  • García-Etxebarria, Iñaki; Regalado, Diego
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)042

Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking
book, January 1980


OnS-duality in Abelian gauge theory
journal, September 1995


Naturalness versus supersymmetric non-renormalization theorems
journal, December 1993


Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994


Anomaly of the Electromagnetic Duality of Maxwell Theory
journal, October 2019


N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories
journal, October 2017

  • Agarwal, Prarit; Sciarappa, Antonio; Song, Jaewon
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)211

Gauge theories from principally extended disconnected gauge groups
journal, March 2019


Resolving spacetime singularities in flux compactifications & KKLT
journal, August 2021


Liouville Field Theory: a Decade After the Revolution
journal, July 2004


1-form symmetries of 4d N=2 class S theories
journal, January 2021


Discrete and higher-form symmetries in SCFTs from wrapped M5-branes
journal, March 2021

  • Bah, Ibrahima; Bonetti, Federico; Minasian, Ruben
  • Journal of High Energy Physics, Vol. 2021, Issue 3
  • DOI: 10.1007/JHEP03(2021)196

Solutions of four-dimensional field theories via M-theory
journal, September 1997


N=1 Superconformal Symmetry in Four-Dimensional Quantum Field Theory
journal, March 1999


Central charges of 𝒩 = 2 superconformal field theories in four dimensions
journal, September 2008


Finiteness in rigid supersymmetric theories
journal, April 1984


The ultra-violet finiteness of the N=4 Yang-Mills theory
journal, April 1983


N = 2 $$ \mathcal{N}=2 $$ central charge bounds from 2d chiral algebras
journal, April 2016


F-theory and orientifolds
journal, September 1996


Brane webs and magnetic quivers for SQCD
journal, March 2020

  • Bourget, Antoine; Cabrera, Santiago; Grimminger, Julius F.
  • Journal of High Energy Physics, Vol. 2020, Issue 3
  • DOI: 10.1007/JHEP03(2020)176

Tinkertoys for Gaiotto duality
journal, November 2010

  • Chacaltana, Oscar; Distler, Jacques
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)099

The Yukawa ß-function in N = 1 rigid supersymmetric theories
journal, April 1984


Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators
journal, January 2016


Branes and the Kraft-Procesi transition
journal, November 2016

  • Cabrera, Santiago; Hanany, Amihay
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)175

On short and semi-short representations for four-dimensional superconformal symmetry
journal, September 2003


Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories
journal, May 2000


NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES
journal, February 2013

  • Chacaltana, Oscar; Distler, Jacques; Tachikawa, Yuji
  • International Journal of Modern Physics A, Vol. 28, Issue 03n04
  • DOI: 10.1142/S0217751X1340006X

(2,0) lagrangian structures
journal, November 2019


The Higgs mechanism — Hasse diagrams for symplectic singularities
journal, January 2020

  • Bourget, Antoine; Cabrera, Santiago; Grimminger, Julius F.
  • Journal of High Energy Physics, Vol. 2020, Issue 1
  • DOI: 10.1007/JHEP01(2020)157

N = 2 superconformal field theory with ADE global symmetry on a D3-brane probe
journal, September 1999


Matrix description of M-theory on T4 and T5
journal, September 1997


On the superconformal index of Argyres–Douglas theories
journal, December 2015


OPEs and 3-point correlators of protected operators in N=4 SYM
journal, April 2002


On mirror symmetry in three dimensional Abelian gauge theories
journal, April 1999


Higgs Branches of rank-0 5d theories from M-theory on (Aj, Al) and (Ak, Dn) singularities
journal, March 2022

  • De Marco, Mario; Sangiovanni, Andrea
  • Journal of High Energy Physics, Vol. 2022, Issue 3
  • DOI: 10.1007/JHEP03(2022)099

Bonus symmetry and the operator product expansion of super-Yang-Mills
journal, October 1999


Holography for non-critical superstrings
journal, October 1999


Theta, time reversal and temperature
journal, May 2017

  • Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)091

Exact results for supersymmetric abelian vortex loops in 2 + 1 dimensions
journal, June 2013

  • Kapustin, Anton; Willett, Brian; Yaakov, Itamar
  • Journal of High Energy Physics, Vol. 2013, Issue 6
  • DOI: 10.1007/JHEP06(2013)099

Geometric Construction ofN = 2 Gauge Theories
journal, January 1999


Twin conformal field theories
journal, March 2019

  • Borsten, L.; Duff, M. J.; Marrani, A.
  • Journal of High Energy Physics, Vol. 2019, Issue 3
  • DOI: 10.1007/JHEP03(2019)112

4D $\mathcal{N} = 2$ SCFT and singularity theory. Part II: complete intersection
journal, January 2017

  • Chen, Bingyi; Xie, Dan; Yau, Shing-Tung
  • Advances in Theoretical and Mathematical Physics, Vol. 21, Issue 1
  • DOI: 10.4310/ATMP.2017.v21.n1.a2

Argyres–Douglas theories, S 1 reductions, and topological symmetries
journal, December 2015


Associated Varieties of Modules Over Kac-Moody Algebras and C2-Cofiniteness of W-Algebras
journal, February 2015


Geometric engineering of quantum field theories
journal, July 1997


Probing F-theory with branes
journal, October 1996


Orientifold points in M theory
journal, October 1999


The Higgs branch of impurity theories
journal, January 1998

  • Kapustin, Anton; Sethi, Savdeep
  • Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 3
  • DOI: 10.4310/ATMP.1998.v2.n3.a6

Asymptotically free = 2 theories and irregular conformal blocks
journal, December 2013


W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes
journal, April 2021


The refined topological vertex
journal, October 2009


Compactifications of F-theory on Calabi-Yau threefolds (II)
journal, September 1996


Localization techniques in quantum field theories
journal, October 2017

  • Pestun, Vasily; Zabzine, Maxim; Benini, Francesco
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 44
  • DOI: 10.1088/1751-8121/aa63c1

{\mathcal N}=2 S-duality via outer-automorphism twists
journal, April 2011


Supersymmetry algebras that include topological charges
journal, September 1978


Notes on S-folds and N $$ \mathcal{N} $$ = 3 theories
journal, September 2016

  • Agarwal, Prarit; Amariti, Antonio
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)032

Conformal manifolds and 3d mirrors of (Dn, Dm) theories
journal, February 2022

  • Carta, Federico; Giacomelli, Simone; Mekareeya, Noppadol
  • Journal of High Energy Physics, Vol. 2022, Issue 2
  • DOI: 10.1007/JHEP02(2022)014

Classification of 4d $ \mathcal{N} $ =2 gauge theories
journal, December 2013

  • Bhardwaj, Lakshya; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)100

${{{\mathcal N}}=2}$ SUSY gauge theories on S 4
journal, October 2017


Supersymmetries and their representations
journal, March 1978


Exact Classical Solution for the 't Hooft Monopole and the Julia-Zee Dyon
journal, September 1975


Stress-tensor OPE in N = 2 $$ \mathcal{N}=2 $$ superconformal theories
journal, February 2016

  • Liendo, Pedro; Ramírez, Israel; Seo, Jihye
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)019

Half-BPS supergravity solutions and superalgebras
journal, December 2008


On Arnold’s 14 ‘exceptional’ $ \mathcal{N} = 2 $ superconformal gauge theories
journal, October 2011

  • Cecotti, Sergio; Del Zotto, Michele
  • Journal of High Energy Physics, Vol. 2011, Issue 10
  • DOI: 10.1007/JHEP10(2011)099

4d $ \mathcal{N} $ = 2 superconformal linear quivers with type IIA duals
journal, August 2012

  • Aharony, Ofer; Berdichevsky, Leon; Berkooz, Micha
  • Journal of High Energy Physics, Vol. 2012, Issue 8
  • DOI: 10.1007/JHEP08(2012)131

N = 3 $$ \mathcal{N}=3 $$ four dimensional field theories
journal, March 2016

  • García-Etxebarria, Iñaki; Regalado, Diego
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)083

Terminal singularities, Milnor numbers, and matter in F-theory
journal, January 2018


Extended superspace, higher derivatives and SL (2, Z) duality
journal, January 1996


New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995


An Index for 4 Dimensional Super Conformal Theories
journal, June 2007

  • Kinney, Justin; Maldacena, Juan; Minwalla, Shiraz
  • Communications in Mathematical Physics, Vol. 275, Issue 1
  • DOI: 10.1007/s00220-007-0258-7

N = 1 supersymmetric mass terms in the N = 4 supersymmetric Yang-Mills theory
journal, March 1983


Tinkertoys for the E 6 theory
journal, September 2015

  • Chacaltana, Oscar; Distler, Jacques; Trimm, Anderson
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)007

A class of finite four-dimensional supersymmetric field theories
journal, April 1983


Super-Weyl anomalies in $ \mathcal{N} $ = 2 supergravity and (non)local effective actions
journal, October 2013


N = 4 Superconformal Bootstrap
journal, August 2013


Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories
journal, July 2021


More on the $ \mathcal{N}=2 $ superconformal systems of type D p (G)
journal, April 2013

  • Cecotti, Sergio; Del Zotto, Michele; Giacomelli, Simone
  • Journal of High Energy Physics, Vol. 2013, Issue 4
  • DOI: 10.1007/JHEP04(2013)153

Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory
journal, March 1997


More Arnold’s $ \mathcal{N} = 2 $ superconformal gauge theories
journal, November 2011


Argyres-Douglas theories, the Macdonald index, and an RG inequality
journal, February 2016

  • Buican, Matthew; Nishinaka, Takahiro
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)159

Deformations of superconformal theories
journal, November 2016

  • Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)135

2-Group symmetries in class S
journal, January 2022


1-form symmetry, isolated $$ \mathcal{N} $$ = 2 SCFTs, and Calabi-Yau threefolds
journal, December 2021

  • Buican, Matthew; Jiang, Hongliang
  • Journal of High Energy Physics, Vol. 2021, Issue 12
  • DOI: 10.1007/JHEP12(2021)024

Higher form symmetries of Argyres-Douglas theories
journal, October 2020

  • Del Zotto, Michele; Etxebarria, Iñaki García; Hosseini, Saghar S.
  • Journal of High Energy Physics, Vol. 2020, Issue 10
  • DOI: 10.1007/JHEP10(2020)056

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, February 2017

  • Maruyoshi, Kazunobu; Song, Jaewon
  • Journal of High Energy Physics, Vol. 2017, Issue 2
  • DOI: 10.1007/JHEP02(2017)075

N $$ \mathcal{N} $$ = 2 S-duality revisited
journal, September 2017

  • Buican, Matthew; Laczko, Zoltan; Nishinaka, Takahiro
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)087

Moduli space of Calabi-Yau manifolds
journal, May 1991


String theory dynamics in various dimensions
journal, June 1995


Branes and the Kraft-Procesi transition: classical case
journal, April 2018

  • Cabrera, Santiago; Hanany, Amihay
  • Journal of High Energy Physics, Vol. 2018, Issue 4
  • DOI: 10.1007/JHEP04(2018)127

Wild quiver gauge theories
journal, February 2012

  • Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro
  • Journal of High Energy Physics, Vol. 2012, Issue 2
  • DOI: 10.1007/JHEP02(2012)031

Landau-Ginzburg skeletons
journal, May 2017

  • Davenport, Ian C.; Melnikov, Ilarion V.
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)050

An N = 2 superconformal fixed point with E6 global symmetry
journal, December 1996


Discrete gauging and Hasse diagrams
journal, August 2021


5d and 4d SCFTs: canonical singularities, trinions and S-dualities
journal, May 2021

  • Closset, Cyril; Giacomelli, Simone; Schäfer-Nameki, Sakura
  • Journal of High Energy Physics, Vol. 2021, Issue 5
  • DOI: 10.1007/JHEP05(2021)274

Superconformal symmetry and representations
journal, January 2021


“Lagrangian” for a Non-Lagrangian Field Theory with N = 2 Supersymmetry
journal, October 2015


On non-renormalization and OPE in superconformal field theories
journal, December 2001


Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003


4d N $$ \mathcal{N} $$ =2 theories with disconnected gauge groups
journal, March 2017

  • Argyres, Philip C.; Martone, Mario
  • Journal of High Energy Physics, Vol. 2017, Issue 3
  • DOI: 10.1007/JHEP03(2017)145

A slow review of the AGT correspondence
journal, August 2022


Central charges and RG flow of strongly-coupled $ \mathcal{N}=2 $ theory
journal, March 2013


Conformal manifolds in four dimensions and chiral algebras
journal, October 2016


Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories
journal, December 2012


3d mirrors of the circle reduction of twisted A2N theories of class S
journal, September 2020

  • Beratto, Emanuele; Giacomelli, Simone; Mekareeya, Noppadol
  • Journal of High Energy Physics, Vol. 2020, Issue 9
  • DOI: 10.1007/JHEP09(2020)161

Three-dimensional gauge theories with supersymmetry enhancement
journal, December 2018


Higher derivative terms, toroidal compactification, and Weyl anomalies in six-dimensional (2, 0) theories
journal, October 2019

  • Córdova, Clay; Dumitrescu, Thomas T.; Yin, Xi
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/JHEP10(2019)128

Improved methods for supergraphs
journal, November 1979


Wall-crossing, Hitchin systems, and the WKB approximation
journal, February 2013


Coulomb branches with complex singularities
journal, June 2018

  • Argyres, Philip C.; Martone, Mario
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/JHEP06(2018)045

Comments on the twisted punctures of Aeven class S theory
journal, June 2018

  • Tachikawa, Yuji; Wang, Yifan; Zafrir, Gabi
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/JHEP06(2018)163

Higher-derivative terms inN= 2 supersymmetric effective actions
journal, July 2003


Matrix theory and U-duality in seven dimensions
journal, May 1997


Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills
journal, January 2014


Introduction to seiberg-witten theory and its stringy origin
journal, May 1997


6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ theories on S 1 /T 2 and class S theories: part II
journal, December 2015

  • Ohmori, Kantaro; Shimizu, Hiroyuki; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)131

Six-dimensional D N theory and four-dimensional SO-USp quivers
journal, July 2009


A holographic computation of the central charges of d = 4, 𝒩 = 2 SCFTs
journal, January 2008


Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994


BPS states of exceptional non-critical strings
journal, September 1997


Magnetic quivers, Higgs branches and 6d $$ \mathcal{N} = \left(1,\kern0.5em 0\right) $$ theories
journal, June 2019

  • Cabrera, Santiago; Hanany, Amihay; Sperling, Marcus
  • Journal of High Energy Physics, Vol. 2019, Issue 6
  • DOI: 10.1007/JHEP06(2019)071

General Argyres-Douglas theory
journal, January 2013


Minimal lectures on two-dimensional conformal field theory
journal, June 2018


Reading between the lines of four-dimensional gauge theories
journal, August 2013

  • Aharony, Ofer; Seiberg, Nathan; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)115

5d and 6d SCFTs have no weak coupling limit
journal, September 2019


On the compactification of 5d theories to 4d
journal, August 2021


Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

  • Beem, Christopher; Lemos, Madalena; Liendo, Pedro
  • Communications in Mathematical Physics, Vol. 336, Issue 3
  • DOI: 10.1007/s00220-014-2272-x

Tinkertoys for the twisted D-series
journal, April 2015

  • Chacaltana, Oscar; Distler, Jacques; Trimm, Anderson
  • Journal of High Energy Physics, Vol. 2015, Issue 4
  • DOI: 10.1007/JHEP04(2015)173

Towards a classification of rank r $$ \mathcal{N} $$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch
journal, December 2020

  • Argyres, Philip C.; Martone, Mario
  • Journal of High Energy Physics, Vol. 2020, Issue 12
  • DOI: 10.1007/JHEP12(2020)022

Conformal manifolds and 3d mirrors of Argyres-Douglas theories
journal, August 2021

  • Carta, Federico; Giacomelli, Simone; Mekareeya, Noppadol
  • Journal of High Energy Physics, Vol. 2021, Issue 8
  • DOI: 10.1007/JHEP08(2021)015

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019


On Type IIA geometries dual to SCFTs
journal, August 2011


F-theory at constant coupling
journal, September 1996


Non-renormalization of two and three point correlators of SYM in superspace
journal, May 1999


Study of N = 2 superconformal field theories in 4 dimensions
journal, July 1996


Tropical geometry and five dimensional Higgs branches at infinite coupling
journal, January 2019

  • Cabrera, Santiago; Hanany, Amihay; Yagi, Futoshi
  • Journal of High Energy Physics, Vol. 2019, Issue 1
  • DOI: 10.1007/JHEP01(2019)068

More N = 4 superconformal bootstrap
journal, August 2017


SUSY enhancement from T-branes
journal, December 2018

  • Carta, Federico; Giacomelli, Simone; Savelli, Raffaele
  • Journal of High Energy Physics, Vol. 2018, Issue 12
  • DOI: 10.1007/JHEP12(2018)127

Supersymmetric instanton calculus
journal, October 1985


M5-branes from gauge theories on the 5-sphere
journal, May 2013


Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers
journal, May 2021

  • Akhond, Mohammad; Carta, Federico; Dwivedi, Siddharth
  • Journal of High Energy Physics, Vol. 2021, Issue 5
  • DOI: 10.1007/JHEP05(2021)269

Non-perturbative aspects in supersymmetric gauge theories
journal, May 1988


M5-brane sources, holography, and Argyres-Douglas theories
journal, November 2021

  • Bah, Ibrahima; Bonetti, Federico; Minasian, Ruben
  • Journal of High Energy Physics, Vol. 2021, Issue 11
  • DOI: 10.1007/JHEP11(2021)140

Electric-magnetic duality in supersymmetric non-Abelian gauge theories
journal, February 1995


All unitary ray representations of the conformal group SU(2,2) with positive energy
journal, February 1977

  • Mack, G.
  • Communications in Mathematical Physics, Vol. 55, Issue 1
  • DOI: 10.1007/BF01613145

Extremal correlators and random matrix theory
journal, April 2021

  • Grassi, Alba; Komargodski, Zohar; Tizzano, Luigi
  • Journal of High Energy Physics, Vol. 2021, Issue 4
  • DOI: 10.1007/JHEP04(2021)214

Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
journal, April 2017


Seiberg-Witten theories on ellipsoids
journal, September 2012


Non-perturbative formulas for central functions of supersymmetric gauge theories
journal, August 1998


No go for a flow
journal, May 2020

  • Carta, Federico; Mininno, Alessandro
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)108

(5d RG-flow) trees in the tropical rain forest
journal, March 2021

  • van Beest, Marieke; Bourget, Antoine; Eckhard, Julius
  • Journal of High Energy Physics, Vol. 2021, Issue 3
  • DOI: 10.1007/JHEP03(2021)241

New aspects of Argyres-Douglas theories and their dimensional reduction
journal, March 2021

  • Giacomelli, Simone; Mekareeya, Noppadol; Sacchi, Matteo
  • Journal of High Energy Physics, Vol. 2021, Issue 3
  • DOI: 10.1007/JHEP03(2021)242

New = 2 superconformal field theories in four dimensions
journal, February 1996


Higher-form symmetries and their anomalies in M-/F-theory duality
journal, December 2021


A non-renormalization theorem for chiral primary 3-point functions
journal, July 2012

  • Baggio, Marco; de Boer, Jan; Papadodimas, Kyriakos
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)137

CFT's from Calabi–Yau four-folds
journal, September 2000


Superconformal index, BPS monodromy and chiral algebras
journal, November 2017

  • Cecotti, Sergio; Song, Jaewon; Vafa, Cumrun
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)013

Bootstrapping the (A1, A2) Argyres-Douglas theory
journal, March 2018

  • Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)033

S-duality in N = 2 supersymmetric gauge theories
journal, December 2007


Monopole operators in three-dimensional N =4 SYM and mirror symmetry
journal, March 2004


Correlation functions of Coulomb branch operators
journal, January 2017

  • Gerchkovitz, Efrat; Gomis, Jaume; Ishtiaque, Nafiz
  • Journal of High Energy Physics, Vol. 2017, Issue 1
  • DOI: 10.1007/JHEP01(2017)103

New $$ \mathcal{N} $$ = 2 superconformal field theories from $$ \mathcal{S} $$-folds
journal, January 2021

  • Giacomelli, Simone; Meneghelli, Carlo; Peelaers, Wolfger
  • Journal of High Energy Physics, Vol. 2021, Issue 1
  • DOI: 10.1007/JHEP01(2021)022

Mirror symmetry and line operators
journal, February 2020

  • Dimofte, Tudor; Garner, Niklas; Geracie, Michael
  • Journal of High Energy Physics, Vol. 2020, Issue 2
  • DOI: 10.1007/JHEP02(2020)075

Holography, singularities on orbifolds and 4D N = 2 SQCD
journal, March 2000


A note on instanton counting for N =2 gauge theories with classical gauge groups
journal, May 2004


Representation Theory of W-Algebras and Higgs Branch Conjecture
conference, May 2019


Landscape of Simple Superconformal Field Theories in 4D
journal, March 2019


Aspects of N = 2 supersymmetric gauge theories in three dimensions
journal, August 1997


Bonus symmetries of N = 4 super-Yang-Mills correlation functions via AdS duality
journal, July 1999


Anomalies and fermion zero modes on strings and domain walls
journal, January 1985


The large N limit of Script N = 2,1 field theories from threebranes in F-theory
journal, July 1998


Two 6D origins of 4D SCFTs: Class S and 6D (1, 0) on a torus
journal, October 2022


Higgs branches of 5d rank-zero theories from geometry
journal, October 2021

  • Collinucci, Andrés; De Marco, Mario; Sangiovanni, Andrea
  • Journal of High Energy Physics, Vol. 2021, Issue 10
  • DOI: 10.1007/JHEP10(2021)018

The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD
journal, July 1996


Magnetic quivers from brane webs with O7+-planes
journal, October 2021

  • Akhond, Mohammad; Carta, Federico
  • Journal of High Energy Physics, Vol. 2021, Issue 10
  • DOI: 10.1007/JHEP10(2021)014

Compactifications of 6d N $$ \mathcal{N} $$ = (1, 0) SCFTs with non-trivial Stiefel-Whitney classes
journal, April 2019

  • Ohmori, Kantaro; Tachikawa, Yuji; Zafrir, Gabi
  • Journal of High Energy Physics, Vol. 2019, Issue 4
  • DOI: 10.1007/JHEP04(2019)006

Supersymmetry and non-perturbative beta functions
journal, May 1988


More three dimensional mirror pairs
journal, May 2011


Anomalous dimensions of fields in a supersymmetric quantum field theory at a renormalization group fixed point
journal, July 1993


Generalized global symmetries
journal, February 2015

  • Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)172

Discrete gauge theories of charge conjugation
journal, September 2019


An Introduction To Quantum Field Theory
book, January 2018


Superspace formulation of new non-linear sigma models
journal, June 1984


Holographic aspects of four dimensional N = 2 SCFTs and their marginal deformations
journal, June 2019


Two-dimensional black hole and singularities of CY manifolds
journal, March 1996


Magnetic lattices for orthosymplectic quivers
journal, December 2020

  • Bourget, Antoine; Grimminger, Julius F.; Hanany, Amihay
  • Journal of High Energy Physics, Vol. 2020, Issue 12
  • DOI: 10.1007/JHEP12(2020)092

Lectures on supersymmetric gauge theories and electric-magnetic duality
journal, February 1996


Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6D (2,0) theories
journal, July 2019


(Symplectic) leaves and (5d Higgs) branches in the Poly(go)nesian Tropical Rain Forest
journal, November 2020

  • van Beest, Marieke; Bourget, Antoine; Eckhard, Julius
  • Journal of High Energy Physics, Vol. 2020, Issue 11
  • DOI: 10.1007/JHEP11(2020)124

Superconformal invariants and extended supersymmetry
journal, May 1997


Anomalies of duality groups and extended conformal manifolds
journal, July 2018

  • Seiberg, Nathan; Tachikawa, Yuji; Yonekura, Kazuya
  • Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 7
  • DOI: 10.1093/ptep/pty069

Mirror symmetry and exact solution of 4D $N = 2$ gauge theories: I
journal, January 1997

  • Katz, Sheldon; Mayr, Peter; Vafa, Cumrun
  • Advances in Theoretical and Mathematical Physics, Vol. 1, Issue 1
  • DOI: 10.4310/ATMP.1997.v1.n1.a2

Comments on higher derivative operators in some SUSY field theories
journal, September 1997


Monopole Operators and Mirror Symmetry in Three Dimensions
journal, December 2002


Nonperturbative Green'S Functions in Theories with Extended Superconformal Symmetry
journal, July 1999


Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part I: physical constraints on relevant deformations
journal, February 2018

  • Argyres, Philip; Lotito, Matteo; Lü, Yongchao
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)001

Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows
journal, February 2018

  • Argyres, Philip C.; Lotito, Matteo; Lü, Yongchao
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)002

Geometric constraints on the space of N=2 SCFTs. Part III: enhanced Coulomb branches and central charges
journal, February 2018

  • Argyres, Philip; Lotito, Matteo; Lü, Yongchao
  • Journal of High Energy Physics, Vol. 2018, Issue 2
  • DOI: 10.1007/JHEP02(2018)003

S -folds, string junctions, and 4D N = 2 SCFTs
journal, April 2021


Light-cone superspace and the ultraviolet finiteness of the N=4 model
journal, March 1983


Positivity constraints on anomalies in supersymmetric gauge theories
journal, June 1998


Testing our understanding of SCFTs: a catalogue of rank-2 $$ \mathcal{N} $$ = 2 theories in four dimensions
journal, July 2022


Connecting 5d Higgs branches via Fayet-Iliopoulos deformations
journal, December 2021

  • van Beest, Marieke; Giacomelli, Simone
  • Journal of High Energy Physics, Vol. 2021, Issue 12
  • DOI: 10.1007/JHEP12(2021)202

S-fold magnetic quivers
journal, February 2021

  • Bourget, Antoine; Giacomelli, Simone; Grimminger, Julius F.
  • Journal of High Energy Physics, Vol. 2021, Issue 2
  • DOI: 10.1007/JHEP02(2021)054

Orientifolds, RR torsion, and K-theory
journal, May 2001


F-theoretic vs microscopic description of a conformal $ \mathcal{N} = 2 $ SYM theory
journal, November 2010

  • Billò, Marco; Gallot, Laurent; Lerda, Alberto
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)041

Vertex operator algebras of Argyres-Douglas theories from M5-branes
journal, December 2017

  • Song, Jaewon; Xie, Dan; Yan, Wenbin
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)123

Magnetic quivers for rank 1 theories
journal, September 2020

  • Bourget, Antoine; Grimminger, Julius F.; Hanany, Amihay
  • Journal of High Energy Physics, Vol. 2020, Issue 9
  • DOI: 10.1007/JHEP09(2020)189

6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories on T2 and class S theories. Part I
journal, July 2015

  • Ohmori, Kantaro; Shimizu, Hiroyuki; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)014

The Topological Vertex
journal, September 2004

  • Aganagic, Mina; Klemm, Albrecht; Mari�o, Marcos
  • Communications in Mathematical Physics, Vol. 254, Issue 2
  • DOI: 10.1007/s00220-004-1162-z

Vertex operator algebras, Higgs branches, and modular differential equations
journal, August 2018

  • Beem, Christopher; Rastelli, Leonardo
  • Journal of High Energy Physics, Vol. 2018, Issue 8
  • DOI: 10.1007/JHEP08(2018)114

$4d$ $\mathcal{N} = 2$ SCFT from complete intersection singularity
journal, January 2017

  • Wang, Yifan; Xie, Dan; Yau, Stephen S. -T.
  • Advances in Theoretical and Mathematical Physics, Vol. 21, Issue 3
  • DOI: 10.4310/ATMP.2017.v21.n3.a6

Self-dual strings and N = 2 supersymmetric field theory
journal, October 1996


A remark on the C 2-cofiniteness condition on vertex algebras
journal, November 2010


Mirrors of 3d Sicilian theories
journal, September 2010

  • Benini, Francesco; Tachikawa, Yuji; Xie, Dan
  • Journal of High Energy Physics, Vol. 2010, Issue 9
  • DOI: 10.1007/JHEP09(2010)063

Chiral algebra of the Argyres-Douglas theory from M5 branes
journal, March 2021


Mirror symmetry in three dimensional gauge theories
journal, October 1996


Top down approach to 6D SCFTs
journal, February 2019

  • Heckman, Jonathan J.; Rudelius, Tom
  • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 9
  • DOI: 10.1088/1751-8121/aafc81

Higgs branches of U/SU quivers via brane locking
journal, August 2022

  • Bourget, Antoine; Grimminger, Julius F.; Hanany, Amihay
  • Journal of High Energy Physics, Vol. 2022, Issue 8
  • DOI: 10.1007/JHEP08(2022)061

Miraculous ultraviolet cancellations in supersymmetry made manifest
journal, April 1984


Magnetic quivers from brane webs with O5 planes
journal, July 2020

  • Bourget, Antoine; Grimminger, Julius F.; Hanany, Amihay
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)204

Classification of Argyres-Douglas theories from M5 branes
journal, September 2016


Mirror symmetry and loop operators
journal, November 2015


Nonholomorphic corrections to the one-loop N = 2 super Yang-Mills action
journal, May 1996


Global aspects of electric-magnetic duality
journal, November 1995


New rank-2 Argyres-Douglas theory
journal, October 2021


Correlation functions in conformal Toda field theory I
journal, November 2007


The gravity duals of $ \mathcal{N}=2 $ superconformal field theories
journal, October 2012

  • Gaiotto, Davide; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)189

4d N = 2 S -folds
journal, May 2020


Supersymmetric Yang-Mills theory and integrable systems
journal, February 1996


Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
journal, May 2012


N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations
journal, December 2016

  • Agarwal, Prarit; Maruyoshi, Kazunobu; Song, Jaewon
  • Journal of High Energy Physics, Vol. 2016, Issue 12
  • DOI: 10.1007/JHEP12(2016)103