Chern-Simons Gauge Theory As A String Theory

TL;DR

This paper explores how certain topological field theories, including three-dimensional Chern-Simons gauge theory, can be interpreted as string theories with unique world-sheet models and instanton effects.

Contribution

It demonstrates the string theory interpretation of Chern-Simons gauge theory and related topological models, highlighting their world-sheet descriptions and instanton contributions.

Findings

Chern-Simons theory can be derived from string theory frameworks.

Instanton effects correspond to Wilson line insertions.

A holomorphic analog of Chern-Simons theory also admits a string interpretation.

Abstract

Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time interpretations. For instance, three-dimensional Chern-Simons gauge theory can arise as a string theory. The world-sheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the space-time Chern-Simons theory. A certain holomorphic analog of Chern-Simons theory can also arise as a string theory.