Chern-Simons Theory on the Torus

TL;DR

This paper explicitly computes the state space of SU(2) Chern-Simons theory on a torus with Wilson lines, exploring its relation to conformal field theory and flat connections, providing insights into topological quantum field theory.

Contribution

It provides an explicit computation of the Schrödinger space of states for SU(2) Chern-Simons theory on a torus with Wilson lines, linking it to conformal field theory structures.

Findings

Explicit state space computation for SU(2) Chern-Simons on T^2

Connection with Friedan-Shenker conformal bundle

Existence of a projective flat connection

Abstract

We compute explicitly the Schr\"odinger picture space of states of SU(2) Chern-Simons theory on $T^2\times R$ in the presence of temporal Wilson lines. Relation with Friedan-Shenker bundle of conformal field theory and the existence of a projective flat connection on this bundle is discussed. Talk given by the first author at the XIX International Colloquium on Group Theoretical Methods in Physics, Salamanca (Spain), June 29-July 4, 1992