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

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 $\beta$-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit $\beta =1$ 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 $\beta$-ensembles of matrix models arising in refined topological string theory.

arXiv comment45 pages; v2: References added

References in corpus (37)

• N=2 dualities
• Black Hole Attractors and the Topological String
• Two Dimensional QCD is a String Theory
• Hurwitz numbers and intersections on moduli spaces of curves
• Gauge Theories and Macdonald Polynomials
• Worldsheet Derivation of a Large N Duality
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Two Dimensional QCD as a String Theory
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Twists and Wilson Loops in the String Theory of Two Dimensional QCD
• Knot Homology from Refined Chern-Simons Theory
• Large N 2D Yang-Mills Theory and Topological String Theory
• Extended Holomorphic Anomaly in Gauge Theory
• Balanced Topological Field Theories
• Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces
• The uses of the refined matrix model recursion
• Quantum Curves and D-Modules
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Orientifolds and the Refined Topological String
• Refined Chern-Simons versus Vogel universality
• The formulae of Kontsevich and Verlinde from the perspective of the Drinfeld double
• Wilson Loops in 2D Yang Mills: Euler characters and Loop equations
• Refined Black Hole Ensembles and Topological Strings
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
• Refined Hopf Link Revisited
• Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Monotone orbifold Hurwitz numbers
• Branched Coverings and Interacting Matrix Strings in Two Dimensions
• Topological Field Theory Amplitudes for $A_{N-1}$ Fibration