The general gaugings of maximal d=9 supergravity

TL;DR

This paper constructs the most general maximal gauged supergravity in nine dimensions using the embedding tensor method, detailing its field content, deformation parameters, and constraints, and compares the results with E11 predictions.

Contribution

It provides a comprehensive construction of the general d=9 supergravity with all deformation parameters and constraints, extending previous specific cases and comparing with E11 predictions.

Findings

Identifies 8 independent deformation parameters for the theory.

Derives field strengths and gauge/supersymmetry transformations for electric fields.

Finds an additional doublet of 9-forms predicted by E11 not previously included.

Abstract

We use the embedding tensor method to construct the most general maximal gauged/massive supergravity in d=9 dimensions and to determine its extended field content. Only the 8 independent deformation parameters (embedding tensor components, mass parameters etc.) identified by Bergshoeff \textit{et al.} (an SL(2,R) triplet, two doublets and a singlet can be consistently introduced in the theory, but their simultaneous use is subject to a number of quadratic constraints. These constraints have to be kept and enforced because they cannot be used to solve some deformation parameters in terms of the rest. The deformation parameters are associated to the possible 8-forms of the theory, and the constraints are associated to the 9-forms, all of them transforming in the conjugate representations. We also give the field strengths and the gauge and supersymmetry transformations for the electric fields in the most general case. We compare these results with the predictions of the E11 approach, finding that the latter predicts one additional doublet of 9-forms, analogously to what happens in N=2, d=4,5,6 theories.