nLab
AGT correspondence

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Quantum field theory

String theory

Contents

Idea

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:

References

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

  • 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=1c=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

  • Oscar Chacaltana, Jacques Distler, Tinkertoys for Gaiotto Duality, JHEP 1011:099,2010, (arXiv:1008.5203, [chacaltana:2010ks,MR3046557])

  • Satoshi Nawata, Givental J-functions, Quantum integrable systems, AGT relation with surface operator, arXiv/1408.4132

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

Revised on August 20, 2014 02:36:12 by Zoran Škoda (161.53.130.104)