Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques

Abstract

These are lecture notes of lectures presented at the 1993 Trieste Summer School, dealing with two classes of two-dimensional field theories, (topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these lectures is to exhibit and extract the topological information contained in these theories, and to present a technique (a Weyl integral formula for path integrals) which allows one to calculate directly their partition function and topological correlation functions on arbitrary closed surfaces. Topics dealt with are (among others): solution of Yang-Mills theory on arbitrary surfaces; calculation of intersection numbers of moduli spaces of flat connections; coupling of Yang-Mills theory to coadjoint orbits and intersection numbers of moduli spaces of parabolic bundles; derivation of the Verlinde formula from the G/G model; derivation of the shift k to k+h in the G/G model via the index of the twisted Dolbeault complex.

70 A4 pages, LaTex, IC/93/356

References in corpus (1)

• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model

Cited by in corpus (9)

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• Two-Dimensional Gauge Theory and Matrix Model
• Spontaneous symmetry breaking in pure 2D Yang-Mills theory
• From simplicial Chern-Simons theory to the shadow invariant II
• From simplicial Chern-Simons theory to the shadow invariant I
• Topological Rényi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual