Kökényesi Zoltán (Wigner RMI): Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory

Friday 23 Feb 2018, 14:00 → 16:00 Europe/Budapest

Tanacsterem

A conjecture by Ooguri, Strominger and Vafa states that partition functions of four-dimensional BPS black holes in Type IIA string theory are given by A-model topological string amplitudes, which reduce on special geometries to q-deformed version of two-dimensional U(N) Yang-Mills theory.  We study a more general version of this duality which relates the refined topological string theory motivated by M-theory with

a two parameter deformed Yang-Mills theory.

 

We derive the large N expansion of the refinement of q-deformed U(N) Yang-Mills theory on closed Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to symmetric polynomials with two parameters, called Macdonald polynomials. In the unrefined limit we reproduce the 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 deformation of the theory of branched coverings of Riemann surfaces. We found that the refined partition function is a generating function for certain parameterized Euler characters, which gives back the original Euler characters of covering spaces in the unrefined limit. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and beta-ensembles of matrix models arising in refined topological string theory.