AGT correspondence explained

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 Luis Alday, Davide Gaiotto, and Yuji Tachikawa in 2009.^[1] It was soon extended to a more general relationship between A_N-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]

References

• Alday . Luis . Gaiotto . Davide . Davide Gaiotto. Tachikawa . Yuji . 2010 . Liouville correlation functions from four-dimensional gauge theories . . 91 . 2 . 167–197 . 0906.3219 . 2010LMaPh..91..167A . 10.1007/s11005-010-0369-5 . 15459761 .
• Wyllard . Niclas . 2009 . A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories . . 2009 . 11 . 002 . 10.1088/1126-6708/2009/11/002 . 2009JHEP...11..002W. 0907.2189 . 10459077 .
• Dimofte . Tudor . Gaiotto . Davide . Davide Gaiotto. Gukov . Sergei . Sergei Gukov. 2010 . Gauge theories labelled by three-manifolds . . 325 . 2 . 367–419 . 10.1007/s00220-013-1863-2 . 2014CMaPh.325..367D . 1108.4389 . 10882599 .

Notes and References

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