Wilson Lines from Representations of NQ-Manifolds

TL;DR

This paper extends the concept of Wilson loops and lines to NQ-manifolds, a class of graded supermanifolds with a homological vector field, exploring their properties and potential applications.

Contribution

It introduces a novel framework for defining Wilson loops/lines within NQ-manifolds, generalizing classical differential geometry concepts.

Findings

Defined Wilson loops/lines in NQ-manifolds

Analyzed properties and subtleties of these objects

Outlined potential applications in geometry and physics

Abstract

An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction.