On the dual variables description of Yang-Mills theory

TL;DR

This paper presents a novel duality relation between four-dimensional SO(4) Yang-Mills theory and Einstein gravity, expressing the gauge partition function in terms of gravity variables, and provides a closed-form expression for the gauge theory's partition function.

Contribution

It introduces a new duality framework linking Yang-Mills and gravity partition functions through a specific gauge choice, offering a fresh perspective on gauge-gravity relations.

Findings

Derived a duality between Yang-Mills and gravity partition functions.

Expressed the gauge action as a first-order Hilbert-Palatini action.

Obtained a closed-form expression for the SO(4) gauge theory partition function.

Abstract

The partition function of four dimensional SO(4) Yang-Mills theory is rewritten in terms of variables admitting straightforward relation to the partition function of pure 4D gravity. The gauge action turns into first-order Hilbert-Palatini action for Einstein gravity with a simple extra term added. The proposed relation can be substantiated as a duality for the partition functions provided a special gauge is imposed for the gravity. The same method allows to find a closed expression for the partition function of the SO(4) gauge theory.