Cluster expansion in terms of knots in gauge theories with finite non-Abelian gauge groups

Abstract

The cluster expansion is developed in lattice gauge theories with finite gauge groups in d≥3 dimensions in which the clusters are connected (d−2)-dimensional complexes, i.e., connected (d−2) surfaces that can branch along (d−3) cells. The interaction between them has a knot theoretical interpretation. It is a many-body interaction, depending on the type of knot they form together. For small enough gauge coupling g analyticity of the correlation functions in the variable exp(−1/g2) is proven.