Tensor Gauge Potentials in Loop Space Formulation of Yang-Mills Fields

TL;DR

This paper demonstrates the emergence of an antisymmetric tensor gauge potential in loop space formulation of Yang-Mills theory, acting as a phase transport for monopoles and addressing redundancy in loop variables.

Contribution

It introduces a tensor gauge potential in loop space Yang-Mills theory, linking it to monopole transport and redundancy removal, a novel insight in gauge field formulations.

Findings

Tensor potential appears as a Lagrange multiplier in loop space.

Tensor acts as phase transport for monopoles.

Removes redundancy in loop variable formulation.

Abstract

Abstrac: It is shown that an antisymmetric rank-two tensor gauge potential of the type first found in string and supersymmetry theories occurs also in ordinary Yang-Mills theory when formulated in loop space, where it appears as a Lagrange multiplier for a zero curvature constraint necessary and sufficient for removing the inherent redundancy of loop variables. It is then further shown that the tensor potential acts there as the parallel `phase' transport for monopoles. (hep-th/yymmnnn)