Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit

Abstract

We study the relationship between refined Chern-Simons theory on lens spaces S^3/Z_p and (q,t)-deformed Yang-Mills theory on the sphere S^2. We derive the instanton partition function of (q,t)-deformed U(N) Yang-Mills theory and describe it explicitly as an analytical continuation of the semi-classical expansion of refined Chern-Simons theory. The derivations are based on a generalization of the Weyl character formula to Macdonald polynomials. The expansion is used to formulate q-generalizations of beta-deformed matrix models for refined Chern-Simons theory, as well as conjectural formulas for the chi_y-genus of the moduli space of U(N) instantons on the surface O(-p)--->P^1 for all p which enumerate black hole microstates in refined topological string theory. We study the large N phase structures of the refined gauge theories, and match them with refined topological string theory on the resolved conifold.

19 pages

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Cited by in corpus (4)

• 3d-3d Correspondence Revisited
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
• Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle