Non-Relativistic Solutions of N=2 Gauged Supergravity

TL;DR

The paper addresses constructing supersymmetric non-relativistic vacua within four-dimensional ${\cal N}=2$ gauged supergravity, focusing on Lifshitz and Schrödinger geometries and their AdS$_4$ relatives. By analyzing a canonical model with one vector and one hypermultiplet, the authors show that Lifshitz vacua with $z=2$ arise for purely electric or purely magnetic gaugings, while mixed gaugings yield Schrödinger and AdS$_4$ vacua; they further relate Schrödinger scaling to the mass of the massive vector in the corresponding AdS$_4$ vacuum via $z(z+1)=(mR)^2$. The work provides explicit Lifshitz and Schrödinger solutions, identifies general supersymmetry conditions, and demonstrates that many of these vacua admit embedding in string/M-theory through Sasaki–Einstein reductions or circle reductions, highlighting the universality and potential holographic relevance of these non-relativistic backgrounds. Overall, the results offer a broad, UV-complete framework for non-relativistic holography in ${\cal N}=2$ gauged supergravity with clear connections to higher-dimensional theories and holographic RG flows.

Abstract

We find infinite families of supersymmetric solutions of four dimensional, N=2 gauged supergravity with Lifshitz, Schrodinger and also AdS symmetries. We focus on the canonical example of a single hypermultiplet and a single vector multiplet and find that the spectrum of solutions depends crucially on whether the gaugings are electric or magnetic but to a far milder extent on the strength of the gaugings. For purely electric or purely magnetic gaugings we generically find Lifshitz solutions, while for a mixed gauging we find Schrodinger and AdS solutions. For some of the gaugings the theory has a known lift to string/M-theory thus giving a higher dimensional embedding of our solutions.