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

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.

arXiv comment38 pages, Latex, 1 figure, minor typos corrected

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Cited by in corpus (5)

• On Irregular Singularity Wave Functions and Superconformal Indices
• Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Entanglement entropy and edge modes in topological string theory II: The dual gauge theory story
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory