Algebraic formulation of higher gauge theory

Understand

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.