Quantization of Donaldson-Uhlenbeck-Yau theory

TL;DR

This paper introduces a covariant path-integral quantization method for the Donaldson-Uhlenbeck-Yau gauge theory, linking it to the gauged G/G Kähler WZW model and exploring its relation to anti-self-dual Yang-Mills theory.

Contribution

It presents the first covariant path-integral quantization for the non-Lagrangian Donaldson-Uhlenbeck-Yau theory and connects it to known models like the gauged G/G Kähler WZW.

Findings

Partition function expressed via gauged G/G Kähler WZW model

Established relationship with anti-self-dual Yang-Mills theory

Provides a new quantization framework for Donaldson-Uhlenbeck-Yau equations

Abstract

A covariant path-integral quantization is proposed for the non-Lagrangian gauge theory described by the Donaldson-Uhlenbeck-Yau equation. The corresponding partition function is shown to admit a nice path-integral representation in terms of the gauged G/G K\"ahler WZW model. A relationship with the $J$-formulation of the anti-self-dual Yang-Mills theory is explored.