Off-Shell Covariantization of Algebroid Gauge Theories

TL;DR

The paper develops a unified, supergeometric framework based on QP-manifolds to construct off-shell covariant field strengths and gauge transformations for algebroid gauge theories, enabling Yang–Mills type actions with Lie $n$-algebroid symmetry. By projecting away auxiliary fields and deforming field strengths with lower-curvature terms, the authors achieve off-shell covariance for 4d theories containing a 1-form gauge field and scalars, and they demonstrate this with explicit examples. Key contributions include the Stückelberg formalism, nonabelian gauged nonlinear sigma models, and the Kotov–Strobl model, along with invariant actions and a discussion of gauge-algebra closure. The approach provides a systematic route to covariant higher gauge theories with potential applications to M5-brane effective theories, tensor hierarchies, and related gravitational/gauge constructions.

Abstract

We present a generalized method to construct field strengths and gauge symmetries, which yield a Yang-Mills type action with Lie n-algebroid gauge symmetry. The procedure makes use of off-shell covariantization in a supergeometric setting. We apply this method to the system of a 1-form gauge field and scalar fields with Lie n-algebroid gauge symmetry. We work out some characteristic examples.