Non-Abelian Stokes Theorem for Wilson Loops Associated with General Gauge Groups

TL;DR

This paper presents a general non-Abelian Stokes theorem for Wilson loops in arbitrary semi-simple compact gauge groups, involving a path integral over group space and applicable regardless of loop topology.

Contribution

It introduces a new formula for the non-Abelian Stokes theorem applicable to general gauge groups, including simple expressions similar to the 't Hooft tensor.

Findings

Formula involving a path integral over group space for Wilson loops

Applicability to loops of any topology

Special properties for the fundamental representation of SU(N)

Abstract

A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops. Some simple expressions analogous to the 't Hooft tensor of a magnetic monopole are given for the 2-form of interest. A special property in the case of the fundamental representation of the group SU(N) is pointed out.