N=2 supersymmetric theory in d=4

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introduction

  • A very exiting development in the last 20 years has been the achievement of exact results in N= 2 gauge theories in four dimensions.


history

  • 1994, Seiberg-Witten exact solutions in 4D N= 2 gauge theories in the IR 사이버그와 위튼이 발견한 정확한 해의 발견 (4차원 게이지 장론의 최초의 정확한 해)
  • 2002, Nekrasov, instanton partition function method, microscopic derivation 네크라소프의 인스탄톤 분배함수 방법
  • 2007, Pestun calculate the partition function of $N= 2$ gauge theories on $S^4$ using Localization techniques
  • 2009, Gaioto 끈이론 대응성을 이용해서 대응성 예를 대폭 확장
  • 가이오토 결과의 중요한 후속성과 중 하나인 AGT, Alday-Gaiotto-Tachikawa conjecture
    • the partition functions on $S^4$ of the $T_{g;n}$ theories are equal to Liouville/Toda field theory correlators on the corresponding Riemann surface


memo

  • the Lagrangian and the Seiberg-Witten solutions of SU(2) gauge theories
  • Argyres-Douglas CFTs and Gaiotto dualities


related items

encyclopedia


expositions

  • Szabo, Richard J. “N=2 Gauge Theories, Instanton Moduli Spaces and Geometric Representation Theory.” arXiv:1507.00685 [hep-Th, Physics:math-Ph], July 2, 2015. http://arxiv.org/abs/1507.00685.
  • Cecotti, Sergio, and Michele Del Zotto. “$Y$ Systems, $Q$ Systems, and 4D $\mathcal{N}=2$ Supersymmetric QFT.” arXiv:1403.7613 [hep-Th], March 29, 2014. http://arxiv.org/abs/1403.7613.
  • Gaiotto, Davide. “Families of N=2 Field Theories.” arXiv:1412.7118 [hep-Th], December 22, 2014. http://arxiv.org/abs/1412.7118.
  • Teschner, Jörg. ‘Exact Results on N=2 Supersymmetric Gauge Theories’. arXiv:1412.7145 [hep-Th], 22 December 2014. http://arxiv.org/abs/1412.7145.
  • Tachikawa, Yuji. 2013. “N=2 Supersymmetric Dynamics for Dummies.” arXiv:1312.2684 [hep-Th] (December 10). http://arxiv.org/abs/1312.2684.
  • Moore, Gregory W. 2012. “Four-Dimensional N=2 Field Theory and Physical Mathematics.” arXiv:1211.2331 [hep-Th, Physics:math-Ph] (November 10). http://arxiv.org/abs/1211.2331.
  • Moore, Surface Defects and the BPS Spectrum of 4d N=2 Theories
  • 2009. Recent progress in N=2 4d field theory
  • Guica, Monica, and Andrew Strominger. 2007. “Cargèse Lectures on String Theory with Eight Supercharges.” Nuclear Physics B. Proceedings Supplement 171: 39–68. doi:10.1016/j.nuclphysbps.2007.06.007.
  • D’Hoker, Eric, and D. H. Phong. 1999. “Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems.” arXiv:hep-th/9912271 (December 29). http://arxiv.org/abs/hep-th/9912271.
  • Lerche, W. 1997. “Introduction to Seiberg-Witten Theory and Its Stringy Origin.” Fortschritte Der Physik. Progress of Physics 45 (3-4): 293–340. doi:10.1002/prop.2190450304.

articles

  • Alexandrov, Sergei, and Boris Pioline. “Theta Series, Wall-Crossing and Quantum Dilogarithm Identities.” arXiv:1511.02892 [hep-Th, Physics:math-Ph], November 9, 2015. http://arxiv.org/abs/1511.02892.
  • Chang, Chih-Kai, Heng-Yu Chen, Dharmesh Jain, and Norton Lee. “Connecting Localization and Wall-Crossing via D-Branes.” arXiv:1512.02645 [hep-Th], December 8, 2015. http://arxiv.org/abs/1512.02645.
  • Lü, Yongchao. “On the Classification of Planar Rank-1 d=4 N=2 Superconformal Field Theories.” arXiv:1511.00669 [hep-Th], November 2, 2015. http://arxiv.org/abs/1511.00669.
  • Cecotti, Sergio, Jaewon Song, Cumrun Vafa, and Wenbin Yan. “Superconformal Index, BPS Monodromy and Chiral Algebras.” arXiv:1511.01516 [hep-Th], November 4, 2015. http://arxiv.org/abs/1511.01516.
  • Bourdier, Jun, Nadav Drukker, and Jan Felix. “The $\mathcal{N}=2$ Schur Index from Free Fermions.” arXiv:1510.07041 [hep-Th], October 23, 2015. http://arxiv.org/abs/1510.07041.
  • Degtyarev, Denis. “On the Moduli Space of Higgs Pairs with Nilpotent Residues.” arXiv:1510.07552 [math-Ph], October 26, 2015. http://arxiv.org/abs/1510.07552.
  • Xie, Dan, and Shing-Tung Yau. “Semicontinuity of 4d N=2 Spectrum under Renormalization Group Flow.” arXiv:1510.06036 [hep-Th], October 20, 2015. http://arxiv.org/abs/1510.06036.
  • Lemos, Madalena, and Pedro Liendo. “Bootstrapping ${\mathcal N}=2$ Chiral Correlators.” arXiv:1510.03866 [hep-Th], October 13, 2015. http://arxiv.org/abs/1510.03866.
  • Drukker, Nadav. “The ${\cal N}=4$ Schur Index with Polyakov Loops.” arXiv:1510.02480 [hep-Th], October 8, 2015. http://arxiv.org/abs/1510.02480.
  • Xie, Dan, and Shing-Tung Yau. “4d N=2 SCFT and Singularity Theory Part I: Classification.” arXiv:1510.01324 [hep-Th], October 5, 2015. http://arxiv.org/abs/1510.01324.
  • Hollowood, Timothy J., and S. Prem Kumar. “Partition Function of N=2* SYM on a Large Four-Sphere.” arXiv:1509.00716 [hep-Th], September 2, 2015. http://arxiv.org/abs/1509.00716.
  • Bershtein, Mikhail, Giulio Bonelli, Massimiliano Ronzani, and Alessandro Tanzini. “Exact Results for ${\cal N}=2$ Supersymmetric Gauge Theories on Compact Toric Manifolds and Equivariant Donaldson Invariants.” arXiv:1509.00267 [hep-Th, Physics:math-Ph], September 1, 2015. http://arxiv.org/abs/1509.00267.
  • Liendo, Pedro, Israel Ramirez, and Jihye Seo. “Stress-Tensor OPE in N=2 Superconformal Theories.” arXiv:1509.00033 [hep-Th], August 31, 2015. http://arxiv.org/abs/1509.00033.
  • Bourdier, Jun, Nadav Drukker, and Jan Felix. “The Exact Schur Index of $\mathcal{N}=4$ SYM.” arXiv:1507.08659 [hep-Th], July 30, 2015. http://arxiv.org/abs/1507.08659.
  • Cordova, Clay, and Shu-Heng Shao. ‘Schur Indices, BPS Particles, and Argyres-Douglas Theories’. arXiv:1506.00265 [hep-Th], 31 May 2015. http://arxiv.org/abs/1506.00265.
  • Cecotti, Sergio, and Michele Del Zotto. ‘Galois Covers of N=2 BPS Spectra and Quantum Monodromy’. arXiv:1503.07485 [hep-Th], 25 March 2015. http://arxiv.org/abs/1503.07485.
  • Cecotti, Sergio, Andrew Neitzke, and Cumrun Vafa. ‘Twistorial Topological Strings and a Tt* Geometry for N=2 Theories in 4d’. arXiv:1412.4793 [hep-Th], 15 December 2014. http://arxiv.org/abs/1412.4793.
  • Cecotti, Sergio, Andrew Neitzke, and Cumrun Vafa. “R-Twisting and 4d/2d Correspondences.” arXiv:1006.3435 [hep-Th], June 17, 2010. http://arxiv.org/abs/1006.3435.

early developments

  • Gaiotto, Davide. “N=2 Dualities.” Journal of High Energy Physics 2012, no. 8 (August 2012). doi:10.1007/JHEP08(2012)034.
  • Pestun, Vasily. “Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops.” Communications in Mathematical Physics 313, no. 1 (July 2012): 71–129. doi:10.1007/s00220-012-1485-0.
  • Nekrasov, Nikita A. “Seiberg-Witten Prepotential From Instanton Counting.” arXiv:hep-th/0206161, June 18, 2002. http://arxiv.org/abs/hep-th/0206161.
  • Seiberg, N., and E. Witten. “Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD.” Nuclear Physics B 431, no. 3 (December 1994): 484–550. doi:10.1016/0550-3213(94)90214-3.
  • Seiberg, N., and E. Witten. “Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory.” Nuclear Physics B 426, no. 1 (September 1994): 19–52. doi:10.1016/0550-3213(94)90124-4.
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