Extended geometry and gauged maximal supergravity

TL;DR

This paper develops a framework using extended geometry and generalized diffeomorphisms to describe gauged maximal supergravity in four dimensions, deriving fluxes, constraints, and a Ricci scalar linked to the scalar potential.

Contribution

It introduces a covariant generalized Ricci tensor and demonstrates its relation to the supergravity scalar potential, extending the geometric understanding of gauged supergravity.

Findings

Derived dynamical fluxes in extended geometry consistent with supersymmetry

Established quadratic constraints from gauge consistency

Connected Ricci scalar to the supergravity scalar potential

Abstract

We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E_7. Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.