Higher form gauge fields and their nonassociative symmetry algebras

Abstract

We show that geometric theories with $p$-form gauge fields have a nonassociative symmetry structure, extending an underlying Lie algebra. This nonassociativity is controlled by the same Chevalley-Eilenberg cohomology that classifies free differential algebras, $p$-form generalizations of Cartan-Maurer equations. A possible relation with flux backgrounds of closed string theory is pointed out.

8 pages, LaTeX. Shortened review part on extended Lie derivatives and free differential algebras, added computation of the Jacobiator for D=11 supergravity, added references. Matches published version on JHEP

References in corpus (4)

• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• T-duality and closed string non-commutative (doubled) geometry
• Non-associative Deformations of Geometry in Double Field Theory
• 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua

Cited by in corpus (6)

• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Supergravity in the group-geometric framework: a primer
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• Supergravities and Branes from Hilbert-Poincaré Series
• On the $L_{\infty }$ formulation of Chern-Simons theories
• Gauge-invariant theories and higher-degree forms