Generalized Higher Gauge Theory

TL;DR

This paper introduces a generalized higher gauge theory framework using concepts from generalized geometry and Courant algebroids, connecting it to double field theory and the (2,0) superconformal theory.

Contribution

It develops a new formulation of higher gauge theory with generalized geometric structures, including principal 2-bundles and a Chern-Simons action, linking to the (2,0) theory.

Findings

Formulation of generalized higher gauge theory using Courant Lie 2-algebroids.

Interpretation of a 3-Lie algebra model as a generalized higher gauge theory.

Establishment of gauge transformations and actions within this framework.

Abstract

We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid $TM\oplus T^*M$ over some manifold $M$ and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and their infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.