Communications in Mathematical Physics

, Volume 273, Issue 2, pp 317–355 | Cite as

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

  • Sebastian de Haro
  • Sanjaye Ramgoolam
  • Alessandro Torrielli
Article

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.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Sebastian de Haro
    • 1
  • Sanjaye Ramgoolam
    • 2
  • Alessandro Torrielli
    • 3
  1. 1.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutGolmGermany
  2. 2.Department of Physics, Queen MaryUniversity of LondonLondonUK
  3. 3.Institut für PhysikHumboldt Universität zu BerlinBerlinGermany

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