Mapping the G-structures and supersymmetric vacua of five-dimensional N=4 supergravity

TL;DR

This paper classifies supersymmetric vacua of five-dimensional N=4 supergravity using G-structures, identifying new solutions with exotic supersymmetry fractions and connecting to known solutions through truncation.

Contribution

It provides a comprehensive classification of vacua based on G-structures and introduces new supersymmetric solutions involving the gravitino multiplet.

Findings

Classified vacua into R^3, SU(2), and SO(4) structures.

Discovered new solutions with exotic supersymmetry fractions.

Connected N=4 solutions to known two-charge solutions via truncation.

Abstract

We classify the supersymmetric vacua of N=4, d=5 supergravity in terms of G-structures. We identify three classes of solutions: with R^3, SU(2) and generic SO(4) structure. Using the Killing spinor equations, we fully characterize the first two classes and partially solve the latter. With the N=4 graviton multiplet decomposed in terms of N=2 multiplets: the graviton, vector and gravitino multiplets, we obtain new supersymmetric solutions corresponding to turning on fields in the gravitino multiplet. These vacua are described in terms of an SO(5) vector sigma-model coupled with gravity, in three or four dimensions. A new feature of these N=4 vacua, which is not seen from an N=2 point of view, is the possibility for preserving more exotic fractions of supersymmetry. We give a few concrete examples of these new supersymmetric (albeit singular) solutions. Additionally, we show how by truncating the N=4, d=5 set of fields to minimal supergravity coupled with one vector multiplet we recover the known two-charge solutions.