New aspects of gauge-gravity relation

TL;DR

This paper explores a novel connection between four-dimensional pure Yang-Mills theory and gravity, reformulating the gauge theory in terms of gravitational variables and deriving the linear potential from Wilson loops.

Contribution

It introduces a new approach to relate Yang-Mills theory to gravity by rewriting the functional integral in terms of metric and Riemann tensors, providing insights into confinement.

Findings

Reformulation of Yang-Mills in gravitational terms

Derivation of linear potential from Wilson loop

New perspective on gauge-gravity correspondence

Abstract

The relation between four-dimensional $SO(4)$ pure Yang-Mills theory and the gravity is discussed. The functional integral for Yang-Mills theory is rewritten in terms of the gravity metric and Riemann tensors. This relation is shown to also provide a simple way to derive the linear potential resulting from the average Wilson loop in pure Yang-Mills theory.