Constructing Lifshitz solutions from AdS

TL;DR

This paper demonstrates how AdS solutions in certain gravitational theories can be systematically reduced to Lifshitz solutions with z=2, preserving some supersymmetry, and provides explicit examples within string theory frameworks.

Contribution

It establishes a general reduction method from AdS to Lifshitz geometries in supergravity and constructs new supersymmetric Lifshitz solutions within string theory.

Findings

AdS solutions can be reduced to Lifshitz with z=2 in supergravity.

Supersymmetric AdS backgrounds lead to Lifshitz solutions preserving 1/4 of supercharges.

Discovery of a new AdS4 x S1 x T(1,1) solution in type IIB supergravity.

Abstract

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.