Chiral expansion and Macdonald deformation of two‐dimensional Yang‐Mills theory. Issue 11 (3rd November 2016) - Kökényesi, Zoltán; Sinkovics, Annamaria; Szabo, Richard J.
Abstract : The analog of the large N Gross‐Taylor holomorphic string expansion for the refinement of q‐deformed U(N) Yang‐Mills theory on a compact oriented Riemann surface is derived. The authors combine Schur‐Weyl duality for quantum groups with the Etingof‐Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit the chiral expansion of q‐deformed Yang‐Mills theory derived by de Haro, Ramgoolam and Torrielli is reproduced. In the classical limit q = 1, the expansion defines a new β‐deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit β = 1 to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. Abstract : We derive the analog of the large N Gross‐Taylor holomorphic string expansion for the refinement of q ‐deformed U ( N ) Yang‐Mills theory on a compact oriented Riemann surface. The derivation combines Schur‐Weyl duality for quantum groups with the Etingof‐Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q ‐deformed Yang‐Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit q = 1, the expansion defines a new β‐deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit β = 1 to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β‐ensembles of matrix models arising in refined topological string theory.