Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

TL;DR

This paper extends the large N expansion of 2D Yang-Mills theory to a q-deformed setting using Hecke algebras, revealing new algebraic structures and geometric interpretations.

Contribution

It introduces a q-deformation of the chiral Gross-Taylor expansion, replacing symmetric group elements with Hecke algebra objects, and explores the q-deformed Schur-Weyl duality.

Findings

Q-deformed expansion involves Hecke algebra trace functions.

Euler characters of configuration spaces appear in the q-deformed context.

Geometric interpretation of the q-deformed formulas is provided.

Abstract

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces in the expansion persists. We discuss the geometrical meaning of these formulae.