nLab
AGT correspondence

Idea

The AGT correspondence (AGT) is a relation between the partition function of $\mathrm{SU}(2{)}^{n+3g-3}$-N=2 D=4 super Yang-Mills theory and Liouville theory? on an $n$-punctured Riemann surface $C_{g,n}$ of genus $g$ (from which the super Yang-Mills theory is obtained by compactifying the M5-brane 6d (2,0)-supersymmetric QFT on it).

Related concepts

• duality in physics, duality in string theory

• Nekrasov function

References

The original article is

• Luis F. Alday, Davide Gaiotto, Yuji Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories (arXiv:0906.3219)

See also

• A. A. Belavin, M. A. Bershtein, B. L. Feigin, A. V. Litvinov, G. M. Tarnopolsky, Instanton moduli spaces and bases in coset conformal field theory, http://arxiv.org/abs/1111.2803

• Volker Schomerus, Paulina Suchanek, Liouville’s imaginary shadow, arxiv/1210.1856

• A.Mironov, A.Morozov, The power of Nekrasov functions, arxiv/0908.2190

• D. Galakhov, A. Mironov, A. Morozov, S-duality as a beta-deformed Fourier transform, arxiv/1205.4998

• A. Mironov, Spectral duality in integrable systems from AGT conjecture, arxiv/1204.0913

• A. Belavin, V. Belavin, AGT conjecture and integrable structure of conformal field theory for $c=1$, Nucl.Phys.B850:199-213 (2011) arxiv/1102.0343

• A. Belavin, V. Belavin, M. Bershtein, Instantons and 2d Superconformal field theory, arxiv/1106.4001

• Kazunobu Maruyoshi, Quantum integrable systems, matrix models, and AGT correspondence, seminar slides

• Giulio Bonelli, Alessandro Tanzini, Hitchin systems, N=2 gauge theories and W-gravity, arxiv/0909.4031

• Giulio Bonelli, Kazunobu Maruyoshi, Alessandro Tanzini, Quantum Hitchin systems via beta-deformed matrix models, arxiv/1104.4016

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