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In theoretical physics, the AGT correspondence is a relationship between Liouville field theory on a punctured Riemann surface and a certain four-dimensional SU(2) gauge theory obtained by compactifying the 6D (2,0) superconformal field theory on the surface. The relationship was discovered by Alday, Gaiotto, and Tachikawa in 2009.[1] It was soon extended to a more general relationship between AN-1 Toda field theory and SU(N) gauge theories.[2] The idea of the AGT correspondence has also been extended to describe relationships between three-dimensional theories.[3]


  1. ^ Alday, Gaiotto, and Tachikawa 2010
  2. ^ Wyllard 2009
  3. ^ Dimofte, Gaiotto, Gukov 2010


  • Alday, Luis; Gaiotto, Davide; Tachikawa, Yuji (2010). "Liouville correlation functions from four-dimensional gauge theories". Letters in Mathematical Physics. 91 (2): 167–197. arXiv:0906.3219. Bibcode:2010LMaPh..91..167A. doi:10.1007/s11005-010-0369-5.
  • Wyllard, Niclas (2009). "A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories". Journal of High Energy Physics. 11: 002. arXiv:0907.2189. Bibcode:2009JHEP...11..002W. doi:10.1088/1126-6708/2009/11/002.
  • Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei (2010). "Gauge theories labelled by three-manifolds". Communications in Mathematical Physics. 325 (2): 367–419. arXiv:1108.4389. Bibcode:2014CMaPh.325..367D. doi:10.1007/s00220-013-1863-2.