Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory

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• 作者：Zoltá ; n Kö ; ké ; nyesi ; Annamaria Sinkovics and Richard J. Szabo
• 刊名：Fortschritte der Physik
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：64
• 期：11-12
• 页码：823-853
• 全文大小：468K
• ISSN：1521-3978

文摘

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.