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Global Aspects Of Gauged Wess-Zumino-Witten Models

Kentaro Hori

Abstract

A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasi-parabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which relates correlation functions for configurations of different topologies. It gives an important information on the topological sum for the partition and correlation functions.

Global Aspects Of Gauged Wess-Zumino-Witten Models

Abstract

A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasi-parabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which relates correlation functions for configurations of different topologies. It gives an important information on the topological sum for the partition and correlation functions.

Paper Structure

This paper contains 4 theorems, 205 equations.

Key Result

Theorem 1

(1) $W$ acts simply transitively on the set of chambres. (2) If ${\rm H}_{1}, \cdots ,{\rm H}_{l}$ are walls of a chambre ${\rm C}$, for each $i$ there exist a unique root $\alpha_{i}$ such that ${\rm H}_{\alpha_{i}}={\rm H}_{i}$ and that $\alpha_{i}$ takes positive values on ${\rm C}$. (3) The set

Theorems & Definitions (4)

  • Theorem 1
  • Proposition 2
  • Theorem 3
  • Proposition 4