Curvatures and potential of M-theory in D=4 with fluxes and twist

TL;DR

This paper analyzes the geometric and physical properties of M-theory compactified to four dimensions on a twisted torus with fluxes, providing explicit curvature formulas, equations of motion, and scalar potentials, highlighting duality symmetries.

Contribution

It introduces two formulations of the FDA for M-theory compactifications with fluxes and twists, and explores the scalar potential's relation to dual formulations with E7(7) symmetry.

Findings

Derived explicit curvatures of the FDA in compactified M-theory.

Presented equations of motion for the bosonic fields.

Established the equivalence of scalar potentials in flat group cases with dual formulations.

Abstract

We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the scalar fields (originating from the 3--form gauge field $\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full $\rE_{7(7)}$ symmetry.