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

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.

arXiv comment11 pages, LaTeX2e

References in corpus (16)

• Two Dimensional Gauge Theories Revisited
• Two Dimensional QCD is a String Theory
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Two Dimensional QCD as a String Theory
• Twists and Wilson Loops in the String Theory of Two Dimensional QCD
• Some Properties of Large $N$ Two Dimensional Yang--Mills Theory
• On the Large N Limit of the Itzykson-Zuber Integral
• Large-N quantum gauge theories in two dimensions
• Large-N limit of the generalized 2-dimensional Yang-Mills theories
• Observables of the generalized 2D Yang-Mills theories on arbitrary surfaces: a path integral approach
• Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N
• $n$-point functions of $2d$ Yang-Mills theories on Riemann surfaces
• Nonlocal two-dimensional Yang-Mills- and generalized Yang-Mills-theories
• On the phase structure of two--dimensional generalized Yang--Mills theories
• Large-N limit of the non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder
• Large-N limit of the generalized 2D Yang-Mills theory on cylinder

Cited by in corpus (4)

• Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit
• Phase structure of the quartic-cubic generalized two dimensional Yang Mills U(N) on the sphere
• Large-N limit of the two-dimensinal Non-Local Yang-Mills theory on arbitrary surfaces with boundary
• Non-local 2D Generalized Yang-Mills theories on arbitrary surfaces with boundary