Generalizing eleven-dimensional supergravity

TL;DR

This paper introduces a method to derive eleven-dimensional supergravity equations from T-duality covariant equations, leading to a generalized formulation that includes additional tensor fields, extending the framework of supergravity theories.

Contribution

It presents a novel procedure to obtain U-duality covariant eleven-dimensional supergravity equations, incorporating a new tensor field analogous to non-unimodular vectors in ten dimensions.

Findings

Derived generalized eleven-dimensional supergravity equations with tensor modifications.

Established a connection between T-duality covariant equations and U-duality formulations.

Proposed a framework for extending supergravity theories to higher dimensions.

Abstract

We develop a procedure to reproduce the ten-dimensional generalized supergravity equations from T-duality covariant equations, that facilitates generalization to U-duality covariant formulations of eleven-dimensional supergravity. The latter leads to a modification of the eleven-dimensional supergravity equations with terms that contain a rank-2 tensor field $J^{mn}$ which is the eleven-dimensional analog of the non-unimodularity Killing vector $I^m$ in ten dimensions.