Compactifications on twisted tori with fluxes and free differential algebras

TL;DR

This paper explores the algebraic structures arising in M-theory compactifications on twisted tori with fluxes, focusing on free differential algebras related to gauge potentials and their integrability conditions.

Contribution

It demonstrates how free differential algebras naturally emerge in M-theory compactifications involving twisted tori and fluxes, connecting algebraic structures with physical compactification scenarios.

Findings

Realization of free differential algebras in M-theory compactifications

Derivation of integrability conditions for gauge curvatures

Connection between antisymmetric tensor fields and algebraic structures

Abstract

We describe free differential algebras for non-abelian one and two form gauge potentials in four dimensions deriving the integrability conditions for the corresponding curvatures. We show that a realization of these algebras occurs in M-theory compactifications on twisted tori with constant four-form flux, due to the presence of antisymmetric tensor fields in the reduced theory.