Five-dimensional AGT conjecture and the deformed Virasoro algebra

By H. Awata, Y. Yamada. 2009

267 citations recorded by the source corpus.

We study an analog of the AGT (Alday-Gaiotto-Tachikawa) relation in five dimensions. We conjecture that the instanton partition function of 5D$ \mathcal{N} = 1 $ pure SU(2) gauge theory coincides with the inner product of the Gaiotto-like state in the deformed Virasoro algebra. In four-dimensional case, a relation between the Gaiotto construction and the theory of Braverman and Etingof is also discussed.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/16455a9e2b77db403d8e806f347f1779c5cef15d

How researchers see this paper

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In Geometry and Topology

1. Abhijit Gadde
2. Wenbin Yan
3. Shlomo S. Razamat
4. L. Rastelli
5. K. Maruyoshi
6. S. Yanagida
7. F. Yagi
8. Hiroshi Itoyama

In Nuclear and High Energy Physics

1. Abhijit Gadde
2. Shlomo S. Razamat
3. Wenbin Yan
4. K. Maruyoshi
5. L. Rastelli
6. E. Pomoni
7. F. Yagi
8. V. Mitev

In Statistical and Nonlinear Physics

1. Wenbin Yan
2. Abhijit Gadde
3. L. Rastelli
4. Shlomo S. Razamat
5. E. Pomoni
6. F. Yagi
7. V. Mitev
8. L. Bao

Citations in the corpus

• Non-Lagrangian theories from brane junctions (2013, methodology): “Therefore, the 5D AGTW relation suggests that the Nekrasov partition functions of these gauge theories can be recast19 into the conformal blocks of q-deformed Toda theories with q-deformed WN symmetry [58, 59].”
• The Quiver Matrix Model and 2d-4d Conformal Connection (2009, background): “These are followed by a number of extensive checks and pieces of supporting evidence [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].”
• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial (2010, background): “Our result is related to a conjecture given by Awata and Yamada in [3].”
• Gauge Theories and Macdonald Polynomials (2011, background): “Some recent papers on subjects related to N = 2 gauge theories that discuss Macdonald polynomials are [50, 51, 52].”