On AGT relation in the case of U(3)

By A. Mironov, A. Morozov. 2009

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Abstract We consider the AGT relation (Alday et al., 2009 [1] ), expressing conformal blocks for the Virasoro and W -algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W 3 algebra. The standard set of Nekrasov functions is sufficient only if additional null-vector restriction is imposed on a half of the external W -primaries and this is just the case when the conformal blocks are fully dictated by W -symmetry and do not depend on a particular model. Explicit checks confirm that the AGT relation survives in this restricted case, as expected.

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

View Paper: https://www.semanticscholar.org/paper/faca3de41a90091e71f3e588f0f5e66b85f4de65

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Citations in the corpus

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].”
Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems (2009, background): “By now there is strong evidence [10,11] that this correspondence with Liouville for the SU(2) case, and its generalization to Toda for the SU(n) case is valid.”
Instanton counting with a surface operator and the chain-saw quiver (2011, background): “Recently it was realized that the instanton partition function for the gauge group G = SU(N) is governed by the W-algebra symmetry WN [5, 6, 7].”
On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture (2010, background): “This should explain the AGT conjecture for higher rank groups [44,45].”
Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “In [2,4,5] the situation with N = 2,3 was studied.”
Gauge Theories and Macdonald Polynomials (2011, methodology): “2 According to the celebrated AGT conjecture [7, 8, 9], the 4d partition functions on the Ω-background [10] and on S4 [11] are computed by Liouville/Toda theory on C.”