Large-N limit of the two-dimensional Yang–Mills theory on surfaces with boundaries

2004/04/30 by M. Alimohammadi, Mohammad Khorrami, M. Khorrami
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2004.07.006

published as Nucl.Phys. B696 (2004) 55-65 · 11 pages, LaTeX2e

openalex publication_date 2004/07/22 · arxiv created 2004/08/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The large-N limit of the two-dimensional U(N) Yang-Mills theory on an arbitrary orientable compact surface with boundaries is studied. It is shown that if the holonomies of the gauge field on boundaries are near the identity, then the critical behavior of the system is the same as that of an orientable surface without boundaries with the same genus but with a modified area. The diffenece between this effective area and the real area of the surface is obtained and shown to be a function of the boundary conditions (holonomies) only. A similar result is shown to hold for the group SU(N) and other simple groups.

Related

• Large N limit of the Yang-Mills measure on compact surfaces II: Makeenko-Migdal equations and planar master field
• Surface sums in two-dimensional large-N lattice Yang--Mills: Cancellations and explicit computations for general loops
• The large N limit of the topological susceptibility of Yang-Mills gauge theory
• Two-dimensional Yang-Mills theory via integrable probability
• Surface sums for lattice Yang-Mills in the large-N limit