Supergravities without an Action: Gauging the Trombone

TL;DR

This paper explores supergravity theories where the global scaling symmetry is gauged without an action, leading to new algebraic structures and implications for the cosmological constant and Kac-Moody algebra connections.

Contribution

It develops an algebraic framework for gauging the scaling symmetry in supergravity, including explicit solutions and modified supersymmetry rules, without relying on an action.

Findings

Gauging scaling symmetry introduces positive contributions to the cosmological constant.

Explicit algebraic solutions for maximal supergravity theories in various dimensions.

Modified supersymmetry transformations and equations of motion in three dimensions.

Abstract

We present a systematic account of supergravity theories in which the global scaling symmetry is gauged. This generalizes the standard gaugings of non-abelian off-shell symmetries. A particular feature of these theories is an additional positive contribution to the effective cosmological constant. As the scaling symmetry is an on-shell symmetry, the resulting gaugings do no longer possess an action. We develop the algebraic framework for the maximal theories in various dimensions and construct explicit solutions to the algebraic consistency constraints - related to `pure-spinor-like' structures for the exceptional groups. As an example, we explicitly work out the modified supersymmetry transformation rules and equations of motion in three dimensions. Finally, we speculate about the role of these theories from the perspective of very extended Kac-Moody algebras.