# Algebraic formulation of higher gauge theory

## TL;DR

This paper develops an algebraic framework for higher gauge theories and gauged sigma models using graded commutative algebras, integrating BRST symmetry and suitable for BV and AKSZ constructions.

## Contribution

It introduces a purely algebraic formulation of higher gauge theories based on graded algebras, connecting to L_infty-algebroids and higher Lie groupoids.

## Key findings

- Provides an algebraic approach compatible with BRST and BV formalisms.
- Shows fields as functions on shifted tangent bundles valued in L_infty-algebroids.
- Connects algebraic formulation to geometric higher Lie groupoid models.

## Abstract

In this paper, we present a purely algebraic formulation of higher gauge theory and gauged sigma models based on the abstract theory of graded commutative algebras and their morphisms. The formulation incorporates naturally BRST symmetry and is also suitable for AKSZ type constructions. It is also shown that for a full--fledged BV formulation including ghost degrees of freedom, higher gauge and gauged sigma model fields must be viewed as internal smooth functions on the shifted tangent bundle of a space time manifold valued in a shifted L_infty-algebroid encoding symmetry. The relationship to other formulations where the L_infty-algebroid arises from a higher Lie groupoid by Lie differentiation is highlighted.