Gauged N=4 supergravities

TL;DR

This paper formulates gauged N=4 supergravities in four and five dimensions, providing a unified description with explicit Lagrangians, incorporating known and new gaugings, and detailing their embedding relations across dimensions.

Contribution

It introduces a comprehensive framework for gauged N=4 supergravities with explicit Lagrangians and gaugings, including new classes and their dimensional embeddings.

Findings

Unified description of N=4 supergravities in 4 and 5 dimensions.

Inclusion of known flux compactification gaugings and new classes.

Embedding relations across dimensions showing organization of deformation parameters.

Abstract

We present the gauged N=4 (half-maximal) supergravities in four and five spacetime dimensions coupled to an arbitrary number of vector multiplets. The gaugings are parameterized by a set of appropriately constrained constant tensors, which transform covariantly under the global symmetry groups SL(2) x SO(6,n) and SO(1,1) x SO(5,n), respectively. In terms of these tensors the universal Lagrangian and the Killing Spinor equations are given. The known gaugings, in particular those originating from flux compactifications, are incorporated in the formulation, but also new classes of gaugings are found. Finally, we present the embedding chain of the five dimensional into the four dimensional into the three dimensional gaugings, thereby showing how the deformation parameters organize under the respectively larger duality groups.