Generalized Higher Gauge Theory

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 $TM\oplus T^{\ast }M$ 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.

24 pages, minor corrections, typos fixed, published version

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Cited by in corpus (6)

• Adjusted Parallel Transport for Higher Gauge Theories
• Algebraic formulation of higher gauge theory
• Higher Gauge Theory
• Higher Gauge Theories from Lie n-algebras and Off-Shell Covariantization
• Generalized Higher Gauge Theory and M5-brane dynamics. Proceedings: Higher structures in String and M-theory, Tohoku Forum for Creativity, March 7-11 2016
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies