# Chern-Simons Gauge Invariance and Boundary Conformal Fields

## TL;DR

This paper explores how boundary conditions in non-Abelian Chern-Simons theory necessitate a scalar field to maintain gauge invariance, revealing a gauge/conformal field theory correspondence on the boundary.

## Contribution

It demonstrates the essential role of a scalar companion field in preserving gauge invariance and establishing a gauge/CFT correspondence for non-Abelian Chern-Simons theories with boundaries.

## Key findings

- Scalar field is necessary for gauge invariance at boundary.
- Boundary scalar field exhibits conformal properties.
- Gauge/CFT correspondence holds for compact gauge groups.

## Abstract

The topological non-Abelian Chern-Simons theory with a boundary is shown to require a scalar field companion in order to preserve overall gauge-invariance both in the 3 dimensional manifold, as well as on its boundary. This scalar field, originally being a pure-gauge Chern-Simons excitation that indicates the most general topological gauge structure in the bulk, is found to be crucial for dynamic scalar excitation on the 2 dimensional generic boundary manifold, the latter naturally representing a conformal mode. This gauge/CFT correspondence is general, for a compact gauge group.