An infrared bootstrap of the Schur index with surface defects

Fluder, Martin; Longhi, Pietro

doi:10.1007/JHEP09(2019)062

Title: An infrared bootstrap of the Schur index with surface defects

Abstract

The infrared formula relates the Schur index of a 4d $$\mathcal{N}$$ = 2 theory to its wall-crossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by many types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class $$\mathcal{S}$$ theories of type A₁ engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a “bootstrap” (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.

Authors:

Fluder, Martin ^[1];

^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Tokyo (Japan)
ETH Zurich (Switzerland)

Publication Date:: 2019-09-10

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1596782

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Fluder, Martin, and Longhi, Pietro. An infrared bootstrap of the Schur index with surface defects.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP09(2019)062.

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                    Fluder, Martin, & Longhi, Pietro. An infrared bootstrap of the Schur index with surface defects.  United States.  https://doi.org/10.1007/JHEP09(2019)062

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                    Fluder, Martin, and Longhi, Pietro. Tue .  
"An infrared bootstrap of the Schur index with surface defects".  United States.  https://doi.org/10.1007/JHEP09(2019)062.  https://www.osti.gov/servlets/purl/1596782.

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@article{osti_1596782,

  title        = {An infrared bootstrap of the Schur index with surface defects},

  author       = {Fluder, Martin and Longhi, Pietro},

  abstractNote = {The infrared formula relates the Schur index of a 4d $\mathcal{N}$ = 2 theory to its wall-crossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by many types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class $\mathcal{S}$ theories of type A1 engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a “bootstrap” (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.},

  doi          = {10.1007/JHEP09(2019)062},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 9,

  volume       = 2019,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

Copy to clipboard

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Works referenced in this record:

Phases of N = 2 theories in two dimensions
journal, August 1993

Witten, Edward
Nuclear Physics B, Vol. 403, Issue 1-2
DOI: 10.1016/0550-3213(93)90033-L

N = 2 dualities
journal, August 2012

Gaiotto, Davide
Journal of High Energy Physics, Vol. 2012, Issue 8
DOI: 10.1007/JHEP08(2012)034

Spectral Networks
journal, March 2013

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Annales Henri Poincaré, Vol. 14, Issue 7
DOI: 10.1007/s00023-013-0239-7

On classification ofN=2 supersymmetric theories
journal, December 1993

Cecotti, Sergio; Vafa, Cumrun
Communications in Mathematical Physics, Vol. 158, Issue 3
DOI: 10.1007/BF02096804

2d TQFT structure of the superconformal indices with outer-automorphism twists
journal, March 2013

Mekareeya, Noppadol; Song, Jaewon; Tachikawa, Yuji
Journal of High Energy Physics, Vol. 2013, Issue 3
DOI: 10.1007/JHEP03(2013)171

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions
journal, January 2013

Cecotti, Sergio; Vafa, Cumrun
Surveys in Differential Geometry, Vol. 18, Issue 1
DOI: 10.4310/SDG.2013.v18.n1.a2

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

Klemm, Albrecht; Lerche, Wolfgang; Mayr, Peter
Nuclear Physics B, Vol. 477, Issue 3
DOI: 10.1016/0550-3213(96)00353-7

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

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 431, Issue 3
DOI: 10.1016/0550-3213(94)90214-3

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Nekrasov, Nikita A.
Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5
DOI: 10.4310/ATMP.2003.v7.n5.a4

A new supersymmetric index
journal, November 1992

Cecotti, Sergio; Fendley, Paul; Intriligator, Ken
Nuclear Physics B, Vol. 386, Issue 2
DOI: 10.1016/0550-3213(92)90572-S

Jenkins–Strebel differentials with poles
journal, January 2008

Liu, Jinsong
Commentarii Mathematici Helvetici
DOI: 10.4171/CMH/123

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

Integrable systems and supersymmetric gauge theory
journal, January 1996

Martinec, Emil J.; Warner, Nicholas P.
Nuclear Physics B, Vol. 459, Issue 1-2
DOI: 10.1016/0550-3213(95)00588-9

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

Argyres, Philip C.; Douglas, Michael R.
Nuclear Physics B, Vol. 448, Issue 1-2
DOI: 10.1016/0550-3213(95)00281-V

Gauge Theories and Macdonald Polynomials
journal, November 2012

Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
Communications in Mathematical Physics, Vol. 319, Issue 1
DOI: 10.1007/s00220-012-1607-8

Surface defects and instanton–vortex interaction
journal, July 2017

Gorsky, A.; Le Floch, B.; Milekhin, A.
Nuclear Physics B, Vol. 920
DOI: 10.1016/j.nuclphysb.2017.04.010

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

Córdova, Clay; Shao, Shu-Heng
Journal of High Energy Physics, Vol. 2016, Issue 1
DOI: 10.1007/JHEP01(2016)040

The Self-Duality Equations on a Riemann Surface
journal, July 1987

Hitchin, N. J.
Proceedings of the London Mathematical Society, Vol. s3-55, Issue 1
DOI: 10.1112/plms/s3-55.1.59

The structure of BPS spectra
text, January 2015

Longhi, Pietro
No Publisher Supplied
DOI: 10.7282/T3FQ9ZMF

On the phase transition towards permanent quark confinement
journal, June 1978

't Hooft, G.
Nuclear Physics B, Vol. 138, Issue 1
DOI: 10.1016/0550-3213(78)90153-0

Refined, Motivic, and Quantum
journal, November 2009

Dimofte, Tudor; Gukov, Sergei
Letters in Mathematical Physics, Vol. 91, Issue 1
DOI: 10.1007/s11005-009-0357-9

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

Witten, Edward
Nuclear Physics B, Vol. 500, Issue 1-3
DOI: 10.1016/S0550-3213(97)00416-1

Spectral Networks with Spin
journal, August 2015

Galakhov, Dmitry; Longhi, Pietro; Moore, Gregory W.
Communications in Mathematical Physics, Vol. 340, Issue 1
DOI: 10.1007/s00220-015-2455-0

Geometry and integrability of topological-antitopological fusion
journal, March 1993

Dubrovin, B.
Communications in Mathematical Physics, Vol. 152, Issue 3
DOI: 10.1007/BF02096618

Branes and N = 2 theories in two dimensions
journal, March 1998

Hanany, Amihay; Hori, Kentaro
Nuclear Physics B, Vol. 513, Issue 1-2
DOI: 10.1016/S0550-3213(97)00754-2

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

BPS graphs: from spectral networks to BPS quivers
journal, July 2017

Gabella, Maxime; Longhi, Pietro; Park, Chan Y.
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)032

S-duality and 2d topological QFT
journal, March 2010

Gadde, Abhijit; Pomoni, Elli; Rastelli, Leonardo
Journal of High Energy Physics, Vol. 2010, Issue 3
DOI: 10.1007/JHEP03(2010)032

ADE spectral networks
journal, August 2016

Longhi, Pietro; Park, Chan Y.
Journal of High Energy Physics, Vol. 2016, Issue 8
DOI: 10.1007/JHEP08(2016)087

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

Donagi, Ron; Witten, Edward
Nuclear Physics B, Vol. 460, Issue 2
DOI: 10.1016/0550-3213(95)00609-5

Wall-crossing in coupled 2d-4d systems
journal, December 2012

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Journal of High Energy Physics, Vol. 2012, Issue 12
DOI: 10.1007/JHEP12(2012)082

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

Argyres, Philip C.; Ronen Plesser, M.; Seiberg, Nathan
Nuclear Physics B, Vol. 461, Issue 1-2
DOI: 10.1016/0550-3213(95)00671-0

Ising model andN=2 supersymmetric theories
journal, October 1993

Cecotti, Sergio; Vafa, Cumrun
Communications in Mathematical Physics, Vol. 157, Issue 1
DOI: 10.1007/BF02098023

5D SYM on 3D sphere and 2D YM
journal, October 2012

Kawano, Teruhiko; Matsumiya, Nariaki
Physics Letters B, Vol. 716, Issue 3-5
DOI: 10.1016/j.physletb.2012.08.055

Topological—anti-topological fusion
journal, December 1991

Cecotti, Sergio; Vafa, Cumrun
Nuclear Physics B, Vol. 367, Issue 2
DOI: 10.1016/0550-3213(91)90021-O

Framed BPS states
journal, January 2013

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2
DOI: 10.4310/ATMP.2013.v17.n2.a1

Rigid Surface Operators
journal, January 2010

Gukov, Sergei; Witten, Edward
Advances in Theoretical and Mathematical Physics, Vol. 14, Issue 1
DOI: 10.4310/ATMP.2010.v14.n1.a3

General Argyres-Douglas theory
journal, January 2013

Xie, Dan
Journal of High Energy Physics, Vol. 2013, Issue 1
DOI: 10.1007/JHEP01(2013)100

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

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 426, Issue 1
DOI: 10.1016/0550-3213(94)90124-4

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

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

Pestun, Vasily
Communications in Mathematical Physics, Vol. 313, Issue 1
DOI: 10.1007/s00220-012-1485-0

Loop operators and S-duality from curves on Riemann surfaces
journal, September 2009

Drukker, Nadav; Morrison, David R.; Okuda, Takuya
Journal of High Energy Physics, Vol. 2009, Issue 09
DOI: 10.1088/1126-6708/2009/09/031

Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
journal, January 2010

Alday, Luis F.; Gaiotto, Davide; Gukov, Sergei
Journal of High Energy Physics, Vol. 2010, Issue 1
DOI: 10.1007/JHEP01(2010)113

Gauge theory loop operators and Liouville theory
journal, February 2010

Drukker, Nadav; Gomis, Jaume; Okuda, Takuya
Journal of High Energy Physics, Vol. 2010, Issue 2
DOI: 10.1007/JHEP02(2010)057

Surface operators in $ \mathcal{N} $ = 2 4d gauge theories
journal, November 2012

Gaiotto, Davide
Journal of High Energy Physics, Vol. 2012, Issue 11
DOI: 10.1007/JHEP11(2012)090

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

Four Dimensional Superconformal Index from $q$ -Deformed Two Dimensional Yang-Mills Theory
journal, June 2011

Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
Physical Review Letters, Vol. 106, Issue 24
DOI: 10.1103/PhysRevLett.106.241602

Counting chiral primaries in , superconformal field theories
journal, July 2006

Römelsberger, Christian
Nuclear Physics B, Vol. 747, Issue 3
DOI: 10.1016/j.nuclphysb.2006.03.037

Wall Crossing Invariants from Spectral Networks
journal, December 2017

Longhi, Pietro
Annales Henri Poincaré, Vol. 19, Issue 3
DOI: 10.1007/s00023-017-0635-5

BPS degeneracies and superconformal index in diverse dimensions
journal, November 2014

Iqbal, Amer; Vafa, Cumrun
Physical Review D, Vol. 90, Issue 10
DOI: 10.1103/PhysRevD.90.105031

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Communications in Mathematical Physics, Vol. 299, Issue 1
DOI: 10.1007/s00220-010-1071-2

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories
journal, October 2010

Dimofte, Tudor; Gukov, Sergei; Soibelman, Yan
Letters in Mathematical Physics, Vol. 95, Issue 1
DOI: 10.1007/s11005-010-0437-x

Bootstrapping the superconformal index with surface defects
journal, January 2013

Gaiotto, Davide; Rastelli, Leonardo; Razamat, Shlomo S.
Journal of High Energy Physics, Vol. 2013, Issue 1
DOI: 10.1007/JHEP01(2013)022

Surface defects, the superconformal index and q-deformed Yang-Mills
journal, October 2013

Alday, Luis F.; Bullimore, Mathew; Fluder, Martin
Journal of High Energy Physics, Vol. 2013, Issue 10
DOI: 10.1007/JHEP10(2013)018

Infrared computations of defect Schur indices
journal, November 2016

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/JHEP11(2016)106

Surface defect indices and 2d-4d BPS states
journal, December 2017

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/JHEP12(2017)078

Surface defects and chiral algebras
journal, May 2017

Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
Journal of High Energy Physics, Vol. 2017, Issue 5
DOI: 10.1007/JHEP05(2017)140

Line defect Schur indices, Verlinde algebras and U(1)r fixed points
journal, November 2017

Neitzke, Andrew; Yan, Fei
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/JHEP11(2017)035

The BPS spectrum generator in 2D-4D systems
journal, November 2012

Longhi, Pietro
Journal of High Energy Physics, Vol. 2012, Issue 11
DOI: 10.1007/JHEP11(2012)107

Spectral Networks and Fenchel–Nielsen Coordinates
journal, May 2016

Hollands, Lotte; Neitzke, Andrew
Letters in Mathematical Physics, Vol. 106, Issue 6
DOI: 10.1007/s11005-016-0842-x

2d SCFTs from M2-branes
journal, November 2013

Hori, Kentaro; Park, Chan Y.; Tachikawa, Yuji
Journal of High Energy Physics, Vol. 2013, Issue 11
DOI: 10.1007/JHEP11(2013)147

ADE spectral networks and decoupling limits of surface defects
journal, February 2017

Longhi, Pietro; Park, Chan Y.
Journal of High Energy Physics, Vol. 2017, Issue 2
DOI: 10.1007/JHEP02(2017)011

Orbifold Schur index and IR formula
journal, April 2018

Imamura, Yosuke
Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 4
DOI: 10.1093/ptep/pty025

Line defects, tropicalization, and multi-centered quiver quantum mechanics
journal, September 2014

Córdova, Clay; Neitzke, Andrew
Journal of High Energy Physics, Vol. 2014, Issue 9
DOI: 10.1007/JHEP09(2014)099

Geometric engineering of (framed) BPS states
journal, January 2014

Chuang, Wu-Yen; Diaconescu, Duiliu-Emanuel; Manschot, Jan
Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 5
DOI: 10.4310/ATMP.2014.v18.n5.a3

About the Absence of Exotics and the Coulomb Branch Formula
journal, November 2017

Del Zotto, Michele; Sen, Ashoke
Communications in Mathematical Physics, Vol. 357, Issue 3
DOI: 10.1007/s00220-017-3041-4

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013

Alim, Murad; Cecotti, Sergio; Córdova, Clay
Communications in Mathematical Physics, Vol. 323, Issue 3
DOI: 10.1007/s00220-013-1789-8

$\mathcal{N} = 2$ quantum field theories and their BPS quivers
journal, January 2014

Alim, Murad; Cecotti, Sergio; Córdova, Clay
Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 1
DOI: 10.4310/ATMP.2014.v18.n1.a2

Wilson-’t Hooft operators in four-dimensional gauge theories and $S$ -duality
journal, July 2006

Kapustin, Anton
Physical Review D, Vol. 74, Issue 2
DOI: 10.1103/PhysRevD.74.025005

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

Surface operators and separation of variables
journal, January 2016

Frenkel, Edward; Gukov, Sergei; Teschner, Jörg
Journal of High Energy Physics, Vol. 2016, Issue 1
DOI: 10.1007/JHEP01(2016)179

Exact WKB analysis and cluster algebras
journal, November 2014

Iwaki, Kohei; Nakanishi, Tomoki
Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 47
DOI: 10.1088/1751-8113/47/47/474009

2d index and surface operators
journal, March 2014

Gadde, Abhijit; Gukov, Sergei
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)080

Surface defects and resolvents
journal, September 2013

Gaiotto, Davide; Gukov, Sergei; Seiberg, Nathan
Journal of High Energy Physics, Vol. 2013, Issue 9
DOI: 10.1007/JHEP09(2013)070

The superconformal index and an elliptic algebra of surface defects
journal, October 2014

Bullimore, Mathew; Fluder, Martin; Hollands, Lotte
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)062

The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms
journal, November 1998

Dorey, Nick
Journal of High Energy Physics, Vol. 1998, Issue 11
DOI: 10.1088/1126-6708/1998/11/005

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

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

Wang, Yifan; Xie, Dan
Physical Review D, Vol. 94, Issue 6
DOI: 10.1103/PhysRevD.94.065012

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

Xie, Dan; Zhao, Peng
Journal of High Energy Physics, Vol. 2013, Issue 3
DOI: 10.1007/JHEP03(2013)006

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

Nekrasov-Shatashvili limit of the 5D superconformal index
journal, August 2016

Papageorgakis, Constantinos; Pini, Alessandro; Rodríguez-Gómez, Diego
Physical Review D, Vol. 94, Issue 4
DOI: 10.1103/PhysRevD.94.045007

Exponential networks and representations of quivers
journal, August 2017

Eager, Richard; Selmani, Sam Alexandre; Walcher, Johannes
Journal of High Energy Physics, Vol. 2017, Issue 8
DOI: 10.1007/JHEP08(2017)063

S-duality and the $ \mathcal{N}=2 $ lens space index
journal, October 2013

Razamat, Shlomo S.; Yamazaki, Masahito
Journal of High Energy Physics, Vol. 2013, Issue 10
DOI: 10.1007/JHEP10(2013)048

Down the rabbit hole with theories of class S $$ \mathcal{S} $$
journal, October 2014

Razamat, Shlomo S.; Willett, Brian
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)099

Heterotic surface defects and dualities from 2d/4d indices
journal, October 2014

Chen, Heng-Yu; Chen, Hsiao-Yi
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)004

N = 1 $$ \mathcal{N}=1 $$ theories of class S k $$ {\mathcal{S}}_k $$
journal, July 2015

Gaiotto, Davide; Razamat, Shlomo S.
Journal of High Energy Physics, Vol. 2015, Issue 7
DOI: 10.1007/JHEP07(2015)073

Surface defects as transfer matrices
journal, November 2016

Maruyoshi, Kazunobu; Yagi, Junya
Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 11
DOI: 10.1093/ptep/ptw151

Surface defects and elliptic quantum groups
journal, June 2017

Yagi, Junya
Journal of High Energy Physics, Vol. 2017, Issue 6
DOI: 10.1007/JHEP06(2017)013

Surface Defects in E-String Compactifications and the van Diejen Model
journal, April 2018

Nazzal, Belal; Razamat, Shlomo S.
Symmetry, Integrability and Geometry: Methods and Applications
DOI: 10.3842/SIGMA.2018.036

Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs
journal, December 2018

Razamat, Shlomo S.
Letters in Mathematical Physics, Vol. 109, Issue 6
DOI: 10.1007/s11005-018-01145-9

On the correspondence between surface operators in Argyres-Douglas theories and modules of chiral algebra
journal, March 2019

Nishinaka, Takahiro; Sasa, Shinya; Zhu, Rui-Dong
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/JHEP03(2019)091

5D SYM and 2D q-deformed YM
journal, April 2013

Fukuda, Yasutaka; Kawano, Teruhiko; Matsumiya, Nariaki
Nuclear Physics B, Vol. 869, Issue 3
DOI: 10.1016/j.nuclphysb.2012.12.017

A brief review of the 2d/4d correspondences
journal, October 2017

Tachikawa, Yuji
Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 44
DOI: 10.1088/1751-8121/aa5df8

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

Buican, Matthew; Nishinaka, Takahiro
Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 1
DOI: 10.1088/1751-8113/49/1/015401

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

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
journal, February 2016

Song, Jaewon
Journal of High Energy Physics, Vol. 2016, Issue 2
DOI: 10.1007/JHEP02(2016)045

On irregular singularity wave functions and superconformal indices
journal, September 2017

Buican, Matthew; Nishinaka, Takahiro
Journal of High Energy Physics, Vol. 2017, Issue 9
DOI: 10.1007/JHEP09(2017)066

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

Maruyoshi, Kazunobu; Song, Jaewon
Physical Review Letters, Vol. 118, Issue 15
DOI: 10.1103/PhysRevLett.118.151602

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 $$ \mathcal{N} $$ =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

S-duality and 2d Topological QFT
text, January 2009

Gadde, Abhijit; Pomoni, Elli; Rastelli, Leonardo
arXiv
DOI: 10.48550/arxiv.0910.2225

Framed BPS States
preprint, January 2010

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
arXiv
DOI: 10.48550/arxiv.1006.0146

Spectral networks
text, January 2012

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
arXiv
DOI: 10.48550/arxiv.1204.4824

Schur Indices, BPS Particles, and Argyres-Douglas Theories
text, January 2015

Cordova, Clay; Shao, Shu-Heng
arXiv
DOI: 10.48550/arxiv.1506.00265

BPS Graphs: From Spectral Networks to BPS Quivers
text, January 2017

Gabella, Maxime; Longhi, Pietro; Park, Chan Y.
arXiv
DOI: 10.48550/arxiv.1704.04204

An Index for 4 dimensional Super Conformal Theories
text, January 2005

Kinney, Justin; Maldacena, Juan; Minwalla, Shiraz
arXiv
DOI: 10.48550/arxiv.hep-th/0510251

A New Supersymmetric Index
text, January 1992

Cecotti, Sergio; Fendley, Paul; Intriligator, Ken
arXiv
DOI: 10.48550/arxiv.hep-th/9204102

Phases of $N=2$ Theories In Two Dimensions
text, January 1993

Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9301042

New N=2 Superconformal Field Theories in Four Dimensions
text, January 1995

Argyres, P. C.; Plesser, M. R.; Seiberg, N.
arXiv
DOI: 10.48550/arxiv.hep-th/9511154

Solutions Of Four-Dimensional Field Theories Via M Theory
text, January 1997

Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9703166

Branes and N=2 Theories in Two Dimensions
text, January 1997

Hanany, Amihay; Hori, Kentaro
arXiv
DOI: 10.48550/arxiv.hep-th/9707192

Works referencing / citing this record:

Testing Macdonald index as a refined character of chiral algebra
journal, February 2020

Watanabe, Akimi; Zhu, Rui-Dong
Journal of High Energy Physics, Vol. 2020, Issue 2
DOI: 10.1007/jhep02(2020)004

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Title: An infrared bootstrap of the Schur index with surface defects

Abstract

Citation Formats

Phases of N = 2 theories in two dimensions journal, August 1993

N = 2 dualities journal, August 2012

Spectral Networks journal, March 2013

On classification ofN=2 supersymmetric theories journal, December 1993

2d TQFT structure of the superconformal indices with outer-automorphism twists journal, March 2013

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions journal, January 2013

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

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

Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

A new supersymmetric index journal, November 1992

Jenkins–Strebel differentials with poles journal, January 2008

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

Integrable systems and supersymmetric gauge theory journal, January 1996

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

Gauge Theories and Macdonald Polynomials journal, November 2012

Surface defects and instanton–vortex interaction journal, July 2017

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

The Self-Duality Equations on a Riemann Surface journal, July 1987

The structure of BPS spectra text, January 2015

On the phase transition towards permanent quark confinement journal, June 1978

Refined, Motivic, and Quantum journal, November 2009

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

Spectral Networks with Spin journal, August 2015

Geometry and integrability of topological-antitopological fusion journal, March 1993

Branes and N = 2 theories in two dimensions journal, March 1998

Tinkertoys for Gaiotto duality journal, November 2010

BPS graphs: from spectral networks to BPS quivers journal, July 2017

S-duality and 2d topological QFT journal, March 2010

ADE spectral networks journal, August 2016

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

Wall-crossing in coupled 2d-4d systems journal, December 2012

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

Ising model andN=2 supersymmetric theories journal, October 1993

5D SYM on 3D sphere and 2D YM journal, October 2012

Topological—anti-topological fusion journal, December 1991

Framed BPS states journal, January 2013

Rigid Surface Operators journal, January 2010

General Argyres-Douglas theory journal, January 2013

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

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

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

Loop operators and S-duality from curves on Riemann surfaces journal, September 2009

Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry journal, January 2010

Gauge theory loop operators and Liouville theory journal, February 2010

Surface operators in $ \mathcal{N} $ = 2 4d gauge theories journal, November 2012

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

Four Dimensional Superconformal Index from q -Deformed Two Dimensional Yang-Mills Theory journal, June 2011

Counting chiral primaries in , superconformal field theories journal, July 2006

Wall Crossing Invariants from Spectral Networks journal, December 2017

BPS degeneracies and superconformal index in diverse dimensions journal, November 2014

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory journal, July 2010

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories journal, October 2010

Bootstrapping the superconformal index with surface defects journal, January 2013

Surface defects, the superconformal index and q-deformed Yang-Mills journal, October 2013

Infrared computations of defect Schur indices journal, November 2016

Surface defect indices and 2d-4d BPS states journal, December 2017

Surface defects and chiral algebras journal, May 2017

Line defect Schur indices, Verlinde algebras and U(1)r fixed points journal, November 2017

The BPS spectrum generator in 2D-4D systems journal, November 2012

Spectral Networks and Fenchel–Nielsen Coordinates journal, May 2016

2d SCFTs from M2-branes journal, November 2013

ADE spectral networks and decoupling limits of surface defects journal, February 2017

Orbifold Schur index and IR formula journal, April 2018

Line defects, tropicalization, and multi-centered quiver quantum mechanics journal, September 2014

Geometric engineering of (framed) BPS states journal, January 2014

About the Absence of Exotics and the Coulomb Branch Formula journal, November 2017

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories journal, August 2013

$\mathcal{N} = 2$ quantum field theories and their BPS quivers journal, January 2014

Wilson-’t Hooft operators in four-dimensional gauge theories and S -duality journal, July 2006

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

Surface operators and separation of variables journal, January 2016

Exact WKB analysis and cluster algebras journal, November 2014

2d index and surface operators journal, March 2014

Surface defects and resolvents journal, September 2013

The superconformal index and an elliptic algebra of surface defects journal, October 2014

The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms journal, November 1998

Wild quiver gauge theories journal, February 2012

Phases of N = 2 theories in two dimensions
journal, August 1993

N = 2 dualities
journal, August 2012

Spectral Networks
journal, March 2013

On classification ofN=2 supersymmetric theories
journal, December 1993

2d TQFT structure of the superconformal indices with outer-automorphism twists
journal, March 2013

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions
journal, January 2013

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

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

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

A new supersymmetric index
journal, November 1992

Jenkins–Strebel differentials with poles
journal, January 2008

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

Integrable systems and supersymmetric gauge theory
journal, January 1996

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

Gauge Theories and Macdonald Polynomials
journal, November 2012

Surface defects and instanton–vortex interaction
journal, July 2017

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

The Self-Duality Equations on a Riemann Surface
journal, July 1987

The structure of BPS spectra
text, January 2015

On the phase transition towards permanent quark confinement
journal, June 1978

Refined, Motivic, and Quantum
journal, November 2009

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

Spectral Networks with Spin
journal, August 2015

Geometry and integrability of topological-antitopological fusion
journal, March 1993

Branes and N = 2 theories in two dimensions
journal, March 1998

Tinkertoys for Gaiotto duality
journal, November 2010

BPS graphs: from spectral networks to BPS quivers
journal, July 2017

S-duality and 2d topological QFT
journal, March 2010

ADE spectral networks
journal, August 2016

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

Wall-crossing in coupled 2d-4d systems
journal, December 2012

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

Ising model andN=2 supersymmetric theories
journal, October 1993

5D SYM on 3D sphere and 2D YM
journal, October 2012

Topological—anti-topological fusion
journal, December 1991

Framed BPS states
journal, January 2013

Rigid Surface Operators
journal, January 2010

General Argyres-Douglas theory
journal, January 2013

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

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

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

Loop operators and S-duality from curves on Riemann surfaces
journal, September 2009

Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
journal, January 2010

Gauge theory loop operators and Liouville theory
journal, February 2010

Surface operators in $ \mathcal{N} $ = 2 4d gauge theories
journal, November 2012

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

Four Dimensional Superconformal Index from $q$ -Deformed Two Dimensional Yang-Mills Theory
journal, June 2011

Counting chiral primaries in , superconformal field theories
journal, July 2006

Wall Crossing Invariants from Spectral Networks
journal, December 2017

BPS degeneracies and superconformal index in diverse dimensions
journal, November 2014

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories
journal, October 2010

Bootstrapping the superconformal index with surface defects
journal, January 2013

Surface defects, the superconformal index and q-deformed Yang-Mills
journal, October 2013

Infrared computations of defect Schur indices
journal, November 2016

Surface defect indices and 2d-4d BPS states
journal, December 2017

Surface defects and chiral algebras
journal, May 2017

Line defect Schur indices, Verlinde algebras and U(1)r fixed points
journal, November 2017

The BPS spectrum generator in 2D-4D systems
journal, November 2012

Spectral Networks and Fenchel–Nielsen Coordinates
journal, May 2016

2d SCFTs from M2-branes
journal, November 2013

ADE spectral networks and decoupling limits of surface defects
journal, February 2017

Orbifold Schur index and IR formula
journal, April 2018

Line defects, tropicalization, and multi-centered quiver quantum mechanics
journal, September 2014

Geometric engineering of (framed) BPS states
journal, January 2014

About the Absence of Exotics and the Coulomb Branch Formula
journal, November 2017

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013

$\mathcal{N} = 2$ quantum field theories and their BPS quivers
journal, January 2014

Wilson-’t Hooft operators in four-dimensional gauge theories and $S$ -duality
journal, July 2006

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

Surface operators and separation of variables
journal, January 2016

Exact WKB analysis and cluster algebras
journal, November 2014

2d index and surface operators
journal, March 2014

Surface defects and resolvents
journal, September 2013

The superconformal index and an elliptic algebra of surface defects
journal, October 2014

The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms
journal, November 1998

Wild quiver gauge theories
journal, February 2012

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

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

Infinite Chiral Symmetry in Four Dimensions
journal, January 2015