Kac-Moody Spectrum of (Half-)Maximal Supergravities

TL;DR

This paper explores the relationship between supergravity deformations and specific generators of very extended Kac-Moody algebras, providing new insights into the algebraic structure of supergravity theories.

Contribution

It establishes a detailed correspondence between gaugings, massive deformations, and Kac-Moody algebra generators in half-maximal supergravity, including the role of quadratic constraints.

Findings

Identifies generators related to gaugings and deformations.

Highlights the role of quadratic constraint generators.

Analyzes a truncation linked to gauge transformations.

Abstract

We establish the correspondence between, on one side, the possible gaugings and massive deformations of half-maximal supergravity coupled to vector multiplets and, on the other side, certain generators of the associated very extended Kac-Moody algebras. The difference between generators associated to gaugings and to massive deformations is pointed out. Furthermore, we argue that another set of generators are related to the so-called quadratic constraints of the embedding tensor. Special emphasis is placed on a truncation of the Kac-Moody algebra that is related to the bosonic gauge transformations of supergravity. We give a separate discussion of this truncation when non-zero deformations are present. The new insights are also illustrated in the context of maximal supergravity.