New aspects of gauge-gravity relation

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.

Comments: 20 pages. v2: matching version published in PRD