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

Kökényesi, Zoltán and Sinkovics, Annamária and Szabó, Richárd J. (2013) Refined Chern-Simons theory and (q, t)-deformed Yang-Mills theory : Semi-classical expansion and planar limit. JOURNAL OF HIGH ENERGY PHYSICS (10). pp. 1-18. ISSN 1126-6708

Preview

Text 1306.1707v1.pdf Download (249kB) | Preview

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 >= 1 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.

Actions (login required)

Edit Item