On an integrable deformation of Kapustin-Witten systems

TL;DR

This paper introduces an integrable deformation of the Kapustin-Witten equations using a Weyl-Wigner-Moyal-Groenewold framework, deriving new solutions from known ones and expanding the understanding of these systems.

Contribution

It presents a novel integrable $ ext{ extsterling}$-deformation of the Kapustin-Witten system utilizing a specific mathematical formalism, and constructs new solutions based on existing solutions.

Findings

Derived an integrable $ ext{ extsterling}$-deformation of the Kapustin-Witten equations.

Obtained new solutions to the deformed equations from known solutions.

Demonstrated the applicability of the Weyl-Wigner-Moyal-Groenewold formalism in this context.

Abstract

In this article we study an integrable deformation of the Kapustin-Witten equations. Using the Weyl-Wigner-Moyal-Groenewold description an integrable $\star$-deformation of a Kapustin-Witten system is obtained. Starting from known solutions of the original equations, some solutions to these deformed equations are obtained.