# New T-duality for Chern-Simons Theory

## TL;DR

This paper introduces a novel T-duality connecting four-dimensional and three-dimensional Chern-Simons theories, revealing new relationships and extending to a broader class of topological quantum field theories.

## Contribution

It identifies a new T-duality between 4D and 3D Chern-Simons theories and discusses its implications in string theory and topological quantum field theories.

## Key findings

- Established a T-duality linking 4D and 3D Chern-Simons theories.
- Extended the duality framework to mixed topological/holomorphic theories.
- Provided insights into the relation between different dimensional Chern-Simons models.

## Abstract

It has recently pointed out that a four-dimensional analog of Chern-Simons theory provides an elegant framework for understanding integrable models with spectral parameters. The goal of this short note is to better understand the relation of this theory to the more standard three-dimensional Chern-Simons theory. We point out that two Chern-Simons theories, in four dimensions and three dimensions, are related by a novel T-duality in field theory. We then discuss this T-duality in string theory. Our T-duality prescription applies to a more general class of topological quantum field theories, producing mixed topological/holomorphic theories. This paper is motivated by the observation by C. Vafa.