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

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

2006-03-07

arxiv.org/abs/hep-th/0603056v2

Commun.Math.Phys.273:317-355,2007

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, Latex, 1 figure, minor typos corrected

Scientific paper

10.1007/s00220-007-0232-4

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.

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