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

Zoltán Kökényesi, Annamaria Sinkovics, Richard Joseph Szabo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
4 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)823-853
Number of pages31
JournalFortschritte der Physik
Issue number11-12
Publication statusPublished - 3 Nov 2016

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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