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arXiv · 1306.1707

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

Zoltan Kokenyesi·Annamaria Sinkovics·Richard J. Szabo
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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.

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Zoltan Kokenyesi, Annamaria Sinkovics, Richard J. Szabo. 2013-06-07. Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit. https://doi.org/10.1007/jhep10(2013)067

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