Double Field Theory and N=4 Gauged Supergravity

TL;DR

This paper explores how Double Field Theory, which describes string theory's NS-NS sector on a doubled spacetime, can be reduced to connect with gauged supergravity, revealing that a weaker constraint suffices for gauge symmetry after reduction.

Contribution

It demonstrates that a weaker differential constraint in Double Field Theory is sufficient for gauge symmetry in the reduced supergravity, linking the theory's constraints with the embedding tensor algebraic conditions.

Findings

Weaker differential constraints are sufficient for gauge symmetry in reduced theories.

Scherk-Schwarz reduction connects Double Field Theory with electric gaugings of supergravity.

Residual symmetries match between the reduced theory and effective supergravity.

Abstract

Double Field Theory describes the NS-NS sector of string theory and lives on a doubled spacetime. The theory has a local gauge symmetry generated by a generalization of the Lie derivative for doubled coordinates. For the action to be invariant under this symmetry, a differential constraint is imposed on the fields and gauge parameters, reducing their possible dependence in the doubled coordinates. We perform a Scherk-Schwarz reduction of Double Field Theory, yielding electric gaugings of half-maximal supergravity in four dimensions when integrability conditions are assumed. The residual symmetries of the compactified theory are mapped with the symmetries of the effective theory and the differential constraints of Double Field Theory are compared with the algebraic conditions on the embedding tensor. It is found that only a weaker form of the differential constraint has to be imposed on background fields to ensure the local gauge symmetry of the reduced action.