### 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.

Original language | English |
---|---|

Pages (from-to) | 823-853 |

Number of pages | 31 |

Journal | Fortschritte der Physik |

Volume | 64 |

Issue number | 11-12 |

DOIs | |

Publication status | Published - 3 Nov 2016 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory'. Together they form a unique fingerprint.

## Cite this

*Fortschritte der Physik*,

*64*(11-12), 823-853. https://doi.org/10.1002/prop.201600087