From Loops to Surfaces

TL;DR

This paper explores the mathematical relationship between Wilson loops in SU(N) Yang Mills theory and fermionic systems on loops and surfaces, extending the concept from one-dimensional curves to higher-dimensional submanifolds.

Contribution

It generalizes the generating function for antisymmetric characters of Wilson loops to fermion systems on surfaces, broadening the theoretical framework.

Findings

Partition function of fermions on loops as generating function

Extension to fermion subsystems on higher-dimensional surfaces

Provides background and addresses questions from presentation

Abstract

The generating function for all antisymmetric characters of a Wilson loop matrix in SU(N) Yang Mills theory is the partition function of a fermion living on the curve describing the loop. This generalizes to fermion subsystems living on higher dimensional submanifolds, for example, surfaces. This write-up also contains some extra background, in response to some questions raised during the oral presentation.