Consistent 4-form fluxes for maximal supergravity

TL;DR

This paper introduces new, simplified ansaetze for the 4-form flux in D=11 supergravity, enabling explicit uplift of 4D maximal gauged supergravity solutions and providing a conjectured master formula for the Freund-Rubin term.

Contribution

The authors develop new ansaetze for the 4-form flux that simplify the uplift process and resolve previous antisymmetry issues, advancing the understanding of supergravity uplifts.

Findings

Explicit uplift formulas for 4D supergravity fluxes

A conjectured master formula for the Freund-Rubin term

Resolution of antisymmetry puzzle in flux uplift

Abstract

We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential ansaetze. The ansatz for the Freund-Rubin term allows us to conjecture a `master formula' for the latter in terms of the scalar potential of d=4 gauged supergravity and its first derivative. We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansaetze.