Field Strength Correlators For 2D Yang-Mills Over Riemann Surfaces

1995/10/20 by J. P. Nunes, João P. Nunes, Howard J. Schnitzer +1 · 1 voice
Physics and Astronomy · #High-Energy Particle Collisions Research #Quantum Chromodynamics and Particle Interactions #Theoretical and Computational Physics #hep-th

paper · pdf · doi:10.1142/s0217751x9700253x

published as Int.J.Mod.Phys. A12 (1997) 4743-4768 · final version to appear in Int. Jour. Mod. Phys. A, minor corrections, added a few comments on Wilson loops and non-abelian Stokes theorem

arxiv created 1996/12/03 · openalex publication_date 1997/10/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The path integral computation of field strength correlation functions for two dimensional Yang-Mills theories over Riemann surfaces is studied. The calculation is carried out by abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

Discussions

• As one might expect from the absence of local degrees of freedom, the correlators of 2d Yang-Mills much like the Wilson line expectation values are constants depending on the group's representation th [stackexchange, 5 points]

Related

• Green functions of 2-dimensional Yang-Mills theories on nonorientable surfaces
• 1992 Trieste Lectures on Topological Gauge Theory and Yang-Mills Theory
• Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques
• Topological correlators of SU(2), N=2^* SYM on four-manifolds
• N=2 Supersymmetric QCD and Four Manifolds; (I) the Donaldson and the Seiberg-Witten Invariants