A Vector Non-abelian Chern-Simons Duality

TL;DR

This paper discovers a classical vector non-abelian duality in pure Chern-Simons theory, extending the known abelian self-duality, and relates it to a dual Wess-Zumino-Witten action through dimensional reduction.

Contribution

It introduces a new classical vector non-abelian duality in Chern-Simons theory, expanding the understanding of dualities beyond abelian cases.

Findings

Identifies a classical vector non-abelian duality in Chern-Simons theory.

Shows dimensional reduction leads to a dual Wess-Zumino-Witten action.

Connects non-abelian duality with known two-dimensional models.

Abstract

Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual' action where its coupling constant $k$ is inverted {\it i.e.} $k \leftrightarrow {1 \over k}$. Here a vector non-abelian duality is found in the pure non-abelian Chern-Simons action at the classical level. The dimensional reduction of the dual Chern-Simons action to two-dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.