Non-Abelian Toda field theories from a 4D Chern-Simons theory

TL;DR

This paper derives non-abelian Toda field theories, including sine-Gordon and Liouville models, from a 4D Chern-Simons theory with boundary defects, revealing a geometric origin and parameter relations.

Contribution

It introduces a novel derivation of NATFTs from 4D Chern-Simons theory with specific boundary conditions and defect configurations.

Findings

Derived sine-Gordon and Liouville models from 4D CS theory.

Identified anisotropy parameter with defect separation.

Established geometric interpretation of NATFTs.

Abstract

We derive non-abelian Toda field theories (NATFTs) from a 4d Chern-Simons (CS) theory with two order defects by employing a certain asymptotic boundary condition. The 4d CS theory is characterized by a meromorphic 1-form $\omega$\,. We adopt $\omega$ with two simple poles and no zeros, and each of the order defects is located at each pole. As a result, an anisotropy parameter $\beta^2$ can be identified with the distance between the two defects. As examples, we can derive the (complex) sine-Gordon model and the Liouville theory.