Gauging The Diamond: Integrable Coset Models from Twistor Space

TL;DR

This paper explores the higher-dimensional origins of two-dimensional integrable models, including coset conformal field theories and sine-Gordon models, through an extended twistor space framework involving holomorphic Chern-Simons theory.

Contribution

It extends the twistor space approach to include gaugings, providing a new higher-dimensional perspective on coset CFTs and deriving novel integrable models.

Findings

Derived higher-dimensional origins of coset CFTs.

Constructed new classes of integrable models including sine-Gordon variants.

Linked twistor space formulations to a broader class of 2D theories.

Abstract

Recent work has shown that certain integrable and conformal field theories in two dimensions can be given a higher-dimensional origin from holomorphic Chern-Simons in six dimensions. Along with anti-self-dual Yang-Mills and four-dimensional Chern-Simons, this gives rise to a diamond correspondence of theories. In this work we extend this framework to incorporate models realised through gaugings. As well as describing a higher-dimensional origin of coset CFTs, by choosing the details of the reduction from higher dimensions, we obtain rich classes of two-dimensional integrable models including homogeneous sine-Gordon models and generalisations that are new to the literature.