New aspects of the gauge-gravity relation

The relation between four-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>O</a:mi><a:mo stretchy="false">(</a:mo><a:mn>4</a:mn><a:mo stretchy="false">)</a:mo></a:math> pure Yang-Mills theory and 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.