AGT correspondence



physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Quantum field theory

String theory



The AGT correspondence (AGT 09) is a relation between the partition function of SU(2) n+3g3SU(2)^{n+3g-3}-N=2 D=4 super Yang-Mills theory and Liouville theory on an nn-punctured Riemann surface C g,nC_{g,n} of genus gg (from which the super Yang-Mills theory is obtained by compactifying the worldvolume 6d (2,0)-supersymmetric QFT of two M5-branes, see at N=2 D=4 super Yang-Mills theory, the section Construction by compactification).

More generally, this construction yields something like a decomposition of the 6d (2,0)-superconformal QFT into a 2d SCFT “with values in 4d SYM field theory” (e.g. Tachikawa 10, slide 25 (33 of 54)). Hence composition with any kind of suitable invariant of the 4d field theories yields an actual 2d SCFT, for instance taking the superconformal index in 4d yields a 2d TQFT (GPRR 10). In this picture of “4d-SYM field theory-valued 2d SCFT” one has the following correspondences:


The original articles are

The 2d TQFT obtained from this by forming the 4d index is discussed in

  • Abhijit Gadde, Elli Pomoni, Leonardo Rastelli, Shlomo S. Razamat, S-duality and 2d Topological QFT, JHEP 1003:032, 2010 (arXiv:0910.2225)

Brief surveys include

  • Yuji Tachikawa, M5-branes, 4d gauge theory and 2d CFT, 2010 (pdf)

  • Abhijit Gadde, 𝒩=2\mathcal{N}= 2 Dualities and 2d TQFT 2012 (pdf)

  • Nikolay Bovev, New SCFTs from wrapped branes, 2013 (pdf)

A detailed review is in

  • Rober Rodger, A pedagogical introduction to the AGT conjecture, Master Thesis Utrecht (2013) (pdf)

See also

The AGT correspondence is treated with the help of a Riemann-Hilbert problem in

  • G. Vartanov, J. Teschner, Supersymmetric gauge theories, quantization of moduli spaces of flat connections, and conformal field theory, arxiv/1302.3778

category: physics

Last revised on January 3, 2018 at 02:45:47. See the history of this page for a list of all contributions to it.