Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows

Argyres, Philip C.; Lotito, Matteo; Lü, Yongchao; Martone, Mario

doi:10.1007/jhep02(2018)002

Title: Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows

Abstract

This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional N = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of N = 2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all 28 cases, with the exception of the N f =4 su(2) gauge theory and the E_n SCFTs which were constructed in [2, 3] and [4, 5].

Authors:

Argyres, Philip C. ^[1]; Lotito, Matteo ^[1]; Lü, Yongchao ^[1]; Martone, Mario ^[1]

Univ. of Cincinnati, OH (United States). Physics Dept.

Publication Date:: 2018-02-01

Research Org.:: Univ. of Cincinnati, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1499173

Grant/Contract Number:: SC0011784

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: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Conformal Field Theory; Extended Supersymmetry; Supersymmetric Gauge Theory

Citation Formats


                    Argyres, Philip C., Lotito, Matteo, Lü, Yongchao, and Martone, Mario. Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep02(2018)002.

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                    Argyres, Philip C., Lotito, Matteo, Lü, Yongchao, & Martone, Mario. Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows.  United States.  https://doi.org/10.1007/jhep02(2018)002

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                    Argyres, Philip C., Lotito, Matteo, Lü, Yongchao, and Martone, Mario. Thu .  
"Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows".  United States.  https://doi.org/10.1007/jhep02(2018)002.  https://www.osti.gov/servlets/purl/1499173.

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@article{osti_1499173,

  title        = {Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows},

  author       = {Argyres, Philip C. and Lotito, Matteo and Lü, Yongchao and Martone, Mario},

  abstractNote = {This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional N = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of N = 2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all 28 cases, with the exception of the N f =4 su(2) gauge theory and the En SCFTs which were constructed in [2, 3] and [4, 5].},

  doi          = {10.1007/jhep02(2018)002},

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

  number       = 2,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {2}

}

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https://doi.org/10.1007/jhep02(2018)002

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Cited by: 19 works

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Figures / Tables:

Table 1: The 28 families of deformed planar rank-1 CB geometries consistent with the low energy Dirac quantization condition. Column 2 lists the Kodaira type of the scale invariant CB geometry, column 3 the resulting singularity types under a generic relevant deformation, and column 4 the maximal flavor symmetry ofmore »

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Works referenced in this record:

Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories
journal, January 2008

Argyres, Philip C.; Wittig, John R.
Journal of High Energy Physics, Vol. 2008, Issue 01
DOI: 10.1088/1126-6708/2008/01/074

Quantised Singularities in the Electromagnetic Field
journal, September 1931

Dirac, P. A. M.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 133, Issue 821
DOI: 10.1098/rspa.1931.0130

Superconformal fixed points with En global symmetry
journal, March 1997

Minahan, Joseph A.; Nemeschansky, Dennis
Nuclear Physics B, Vol. 489, Issue 1-2
DOI: 10.1016/S0550-3213(97)00039-4

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

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

Minahan, Joseph A.; Nemeschansku, Dennis
Nuclear Physics B, Vol. 482, Issue 1-2
DOI: 10.1016/S0550-3213(96)00552-4

F-theory at constant coupling
journal, September 1996

Dasgupta, Keshav; Mukhi, Sunil
Physics Letters B, Vol. 385, Issue 1-4
DOI: 10.1016/0370-2693(96)00875-1

Uncovering the symmetries on $[p,q]$ 7-branes: Beyond the Kodaira classification
journal, January 1999

DeWolfe, Oliver; Hauer, Tamás; Iqbal, Amer
Advances in Theoretical and Mathematical Physics, Vol. 3, Issue 6
DOI: 10.4310/ATMP.1999.v3.n6.a5

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

String junctions for arbitrary Lie-algebra representations
journal, March 1999

DeWolfe, Oliver; Zwiebach, Barton
Nuclear Physics B, Vol. 541, Issue 3
DOI: 10.1016/S0550-3213(98)00743-3

Duality and Weyl symmetry of 7-brane configurations
journal, September 2000

Hauer, Tamás; Iqbal, Amer; Zwiebach, Barton
Journal of High Energy Physics, Vol. 2000, Issue 09
DOI: 10.1088/1126-6708/2000/09/042

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

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

Quantum Field Theory of Particles with Both Electric and Magnetic Charges
journal, December 1968

Zwanziger, Daniel
Physical Review, Vol. 176, Issue 5
DOI: 10.1103/PhysRev.176.1489

Probing F-theory with branes
journal, October 1996

Banks, Tom; Douglas, Michael R.; Seiberg, Nathan
Physics Letters B, Vol. 387, Issue 2
DOI: 10.1016/0370-2693(96)00808-8

Invariants of Finite Groups Generated by Reflections
journal, October 1955

Chevalley, Claude
American Journal of Mathematics, Vol. 77, Issue 4
DOI: 10.2307/2372597

Semicontinuity of 4d N = 2 $$ \mathcal{N}=2 $$ spectrum under renormalization group flow
journal, March 2016

Xie, Dan; Yau, Shing-Tung
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/JHEP03(2016)094

A Magnetic Model of Matter
journal, August 1969

Schwinger, J.
Science, Vol. 165, Issue 3895
DOI: 10.1126/science.165.3895.757

F-theory and orientifolds
journal, September 1996

Sen, Ashoke
Nuclear Physics B, Vol. 475, Issue 3
DOI: 10.1016/0550-3213(96)00347-1

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012

Argyres, Philip C.; Ünsal, Mithat
Journal of High Energy Physics, Vol. 2012, Issue 8
DOI: 10.1007/JHEP08(2012)063

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

On the Structure of Compact Complex Analytic Surfaces, II
journal, July 1966

Kodaira, K.
American Journal of Mathematics, Vol. 88, Issue 3
DOI: 10.2307/2373150

All Possible Symmetries of the $S$ Matrix
journal, July 1967

Coleman, Sidney; Mandula, Jeffrey
Physical Review, Vol. 159, Issue 5
DOI: 10.1103/PhysRev.159.1251

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

Finite Unitary Reflection Groups
journal, January 1954

Shephard, G. C.; Todd, J. A.
Canadian Journal of Mathematics, Vol. 6
DOI: 10.4153/CJM-1954-028-3

Finite complex reflection groups
journal, January 1976

Cohen, Arjeh M.
Annales scientifiques de l'École normale supérieure, Vol. 9, Issue 3
DOI: 10.24033/asens.1313

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

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

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

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

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

Masayuki Noguchi,
Nuclear Physics B, Vol. 556, Issue 1-2
DOI: 10.1016/S0550-3213(99)00343-0

Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories
journal, December 2013

Argyres, Philip C.
Journal of Physics: Conference Series, Vol. 462
DOI: 10.1088/1742-6596/462/1/012001

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

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

On the Structure of Compact Complex Analytic Surfaces, I
journal, October 1964

Kodaira, K.
American Journal of Mathematics, Vol. 86, Issue 4
DOI: 10.2307/2373157

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

Argyres, Philip C.; Seiberg, Nathan
Journal of High Energy Physics, Vol. 2007, Issue 12
DOI: 10.1088/1126-6708/2007/12/088

Reflection groups and coxeter groups
text, January 2016

Bingham, Kouver
University of Utah
DOI: 10.26053/0h-8rtg-5500

On the Structure of Compact Complex Analytic Surfaces, ii
journal, June 1964

Kodaira, K.
Proceedings of the National Academy of Sciences, Vol. 51, Issue 6
DOI: 10.1073/pnas.51.6.1100

Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
text, January 2007

Argyres, Philip C.; Wittig, John R.
arXiv
DOI: 10.48550/arxiv.0712.2028

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
text, January 2012

Argyres, Philip C.; Ünsal, Mithat
arXiv
DOI: 10.48550/arxiv.1206.1890

Tinkertoys for the $E_6$ Theory
preprint, January 2014

Chacaltana, Oscar; Distler, Jacques; Trimm, Anderson
arXiv
DOI: 10.48550/arxiv.1403.4604

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

F-theory and Orientifolds
text, January 1996

Sen, Ashoke
arXiv
DOI: 10.48550/arxiv.hep-th/9605150

Probing F-theory With Branes
text, January 1996

Banks, Tom; Douglas, Michael R.; Seiberg, Nathan
arXiv
DOI: 10.48550/arxiv.hep-th/9605199

F-Theory at Constant Coupling
text, January 1996

Dasgupta, Keshav; Mukhi, Sunil
arXiv
DOI: 10.48550/arxiv.hep-th/9606044

An N=2 Superconformal Fixed Point with E_6 Global Symmetry
text, January 1996

Minahan, Joseph A.; Nemeschansky, Dennis
arXiv
DOI: 10.48550/arxiv.hep-th/9608047

Superconformal Fixed Points with E_n Global Symmetry
text, January 1996

Minahan, Joseph A.; Nemeschansky, Dennis
arXiv
DOI: 10.48550/arxiv.hep-th/9610076

String Junctions for Arbitrary Lie Algebra Representations
text, January 1998

DeWolfe, Oliver; Zwiebach, Barton
arXiv
DOI: 10.48550/arxiv.hep-th/9804210

Uncovering the Symmetries on [p,q] 7-branes: Beyond the Kodaira Classification
text, January 1998

DeWolfe, Oliver; Hauer, Tamas; Iqbal, Amer
arXiv
DOI: 10.48550/arxiv.hep-th/9812028

Works referencing / citing this record:

Universal correlation functions in rank 1 SCFTs
journal, December 2019

Hellerman, Simeon; Maeda, Shunsuke; Orlando, Domenico
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)047

Notes on anomalies, elliptic curves and the BS-D conjecture
journal, December 2019

Lü, Yongchao; Minahan, Joseph A.
Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 2
DOI: 10.1088/1751-8121/ab5ac3

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Title: Geometric constraints on the space of N = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows

Abstract

Citation Formats

Figures / Tables:

Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories journal, January 2008

Quantised Singularities in the Electromagnetic Field journal, September 1931

Superconformal fixed points with En global symmetry journal, March 1997

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

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

F-theory at constant coupling journal, September 1996

Uncovering the symmetries on $[p,q]$ 7-branes: Beyond the Kodaira classification journal, January 1999

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

String junctions for arbitrary Lie-algebra representations journal, March 1999

Duality and Weyl symmetry of 7-brane configurations journal, September 2000

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

Tinkertoys for the E 6 theory journal, September 2015

Quantum Field Theory of Particles with Both Electric and Magnetic Charges journal, December 1968

Probing F-theory with branes journal, October 1996

Invariants of Finite Groups Generated by Reflections journal, October 1955

Semicontinuity of 4d N = 2 $$ \mathcal{N}=2 $$ spectrum under renormalization group flow journal, March 2016

A Magnetic Model of Matter journal, August 1969

F-theory and orientifolds journal, September 1996

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects journal, August 2012

Tinkertoys for Gaiotto duality journal, November 2010

On the Structure of Compact Complex Analytic Surfaces, II journal, July 1966

All Possible Symmetries of the S Matrix journal, July 1967

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

Finite Unitary Reflection Groups journal, January 1954

Finite complex reflection groups journal, January 1976

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

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

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

Tinkertoys for the D N series journal, February 2013

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

Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories journal, December 2013

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

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

On the Structure of Compact Complex Analytic Surfaces, I journal, October 1964

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

Reflection groups and coxeter groups text, January 2016

On the Structure of Compact Complex Analytic Surfaces, ii journal, June 1964

Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories text, January 2007

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects text, January 2012

Tinkertoys for the $E_6$ Theory preprint, January 2014

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

F-theory and Orientifolds text, January 1996

Probing F-theory With Branes text, January 1996

F-Theory at Constant Coupling text, January 1996

An N=2 Superconformal Fixed Point with E_6 Global Symmetry text, January 1996

Superconformal Fixed Points with E_n Global Symmetry text, January 1996

String Junctions for Arbitrary Lie Algebra Representations text, January 1998

Uncovering the Symmetries on [p,q] 7-branes: Beyond the Kodaira Classification text, January 1998

Universal correlation functions in rank 1 SCFTs journal, December 2019

Notes on anomalies, elliptic curves and the BS-D conjecture journal, December 2019

Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories
journal, January 2008

Quantised Singularities in the Electromagnetic Field
journal, September 1931

Superconformal fixed points with En global symmetry
journal, March 1997

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

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

F-theory at constant coupling
journal, September 1996

Uncovering the symmetries on $[p,q]$ 7-branes: Beyond the Kodaira classification
journal, January 1999

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

String junctions for arbitrary Lie-algebra representations
journal, March 1999

Duality and Weyl symmetry of 7-brane configurations
journal, September 2000

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

Tinkertoys for the E 6 theory
journal, September 2015

Quantum Field Theory of Particles with Both Electric and Magnetic Charges
journal, December 1968

Probing F-theory with branes
journal, October 1996

Invariants of Finite Groups Generated by Reflections
journal, October 1955

Semicontinuity of 4d N = 2 $$ \mathcal{N}=2 $$ spectrum under renormalization group flow
journal, March 2016

A Magnetic Model of Matter
journal, August 1969

F-theory and orientifolds
journal, September 1996

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012

Tinkertoys for Gaiotto duality
journal, November 2010

On the Structure of Compact Complex Analytic Surfaces, II
journal, July 1966

All Possible Symmetries of the $S$ Matrix
journal, July 1967

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

Finite Unitary Reflection Groups
journal, January 1954

Finite complex reflection groups
journal, January 1976

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

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

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

Tinkertoys for the D N series
journal, February 2013

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

Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories
journal, December 2013

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

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

On the Structure of Compact Complex Analytic Surfaces, I
journal, October 1964

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

Reflection groups and coxeter groups
text, January 2016

On the Structure of Compact Complex Analytic Surfaces, ii
journal, June 1964

Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
text, January 2007

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
text, January 2012

Tinkertoys for the $E_6$ Theory
preprint, January 2014

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

F-theory and Orientifolds
text, January 1996

Probing F-theory With Branes
text, January 1996

F-Theory at Constant Coupling
text, January 1996

An N=2 Superconformal Fixed Point with E_6 Global Symmetry
text, January 1996

Superconformal Fixed Points with E_n Global Symmetry
text, January 1996

String Junctions for Arbitrary Lie Algebra Representations
text, January 1998

Uncovering the Symmetries on [p,q] 7-branes: Beyond the Kodaira Classification
text, January 1998

Universal correlation functions in rank 1 SCFTs
journal, December 2019

Notes on anomalies, elliptic curves and the BS-D conjecture
journal, December 2019