The $\beta$-symmetry of supergravity

TL;DR

This paper introduces the concept of $eta$-symmetry in supergravity, showing it as a hidden bosonic symmetry that preserves the theory's couplings and extends the understanding of non-geometric symmetries in string supergravities.

Contribution

It explicitly defines the $eta$-transformations in supergravity to first order in $eta'$ and demonstrates their invariance and algebraic closure.

Findings

$eta$-symmetry acts as a hidden bosonic symmetry in supergravity.

Explicit $eta$-transformations are derived to first order in $eta'$.

The invariance of the supergravity action under $eta$-transformations is verified.

Abstract

Continuous O$(d,d)$ global symmetries emerge in Kaluza-Klein reductions of $D$-dimensional string supergravities to $D-d$ dimensions. We show that the non-geometric elements of this group effectively act in the $D$-dimensional parent theory as a hidden bosonic symmetry that fixes its couplings: the $\beta$-symmetry. We give the explicit $\beta$-transformations to first order in $\alpha'$ and verify the invariance of the action as well as the closure of the transformation rules.