N=2 supersymmetric theory in d=4

수학노트
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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

  • Bingyi Chen, Dan Xie, Shing-Tung Yau, Stephen S. -T. Yau, Huaiqing Zuo, 4d N=2 SCFT and singularity theory Part II: Complete intersection, arXiv:1604.07843 [hep-th], April 26 2016, http://arxiv.org/abs/1604.07843
  • 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.