Supersymmetric Wilson Lines and Loops, and Super Non-Abelian Stokes Theorem

TL;DR

This paper develops a supersymmetric extension of the Wilson line and loop formalism using Grassmann-valued matrices, and proves a supersymmetric non-Abelian Stokes theorem, advancing the mathematical tools for supersymmetric gauge theories.

Contribution

It introduces a supersymmetric product integral formalism with Grassmann matrices and establishes a supersymmetric non-Abelian Stokes theorem, extending gauge theory techniques.

Findings

Supersymmetric Wilson Lines and Loops are described using Grassmann-valued matrices.

A supersymmetric version of the non-Abelian Stokes theorem is proven.

The formalism provides a natural framework for supersymmetric gauge theories.

Abstract

We generalize the standard product integral formalism to incorporate Grassmann valued matrices and show that the resulting supersymmetric product integrals provide a natural framework for describing supersymmetric Wilson Lines and Wilson Loops. We use this formalism to establish the supersymmetric version of the non-Abelian Stokes theorem.