Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications

TL;DR

This paper reveals that in Kaluza-Klein compactifications, certain metric transformations act like higher-form symmetries, explaining the origin of hidden symmetries and dualities in lower-dimensional theories.

Contribution

It introduces a new perspective on hidden symmetries as higher-form symmetries arising from metric transformations in compactified spacetimes.

Findings

Identifies non-diffeomorphic metric transformations as higher-form symmetries.

Links these symmetries to hidden dualities in reduced theories.

Provides a symmetry-based explanation for dualities in Kaluza-Klein compactifications.

Abstract

We show that, in presence of isometries and non-trivial topology, the Einstein--Hilbert action is invariant under certain transformations of the metric which are not diffeomorphisms. These transformations are similar to the higher-form symmetries of field theories with $p$-form fields. In the context of toroidal Kaluza--Klein compactifications, we show that these symmetries give rise to some of the ``hidden symmetries'' (dualities) of the dimensionally-reduced theories.