Lifshitz solutions in supergravity and string theory

TL;DR

The paper addresses realizing Lifshitz spacetimes with general dynamical exponent $z\ge 1$ within string theory. The authors adopt a bottom-up strategy by first constructing $Li_q \times \Omega_{d-q}$ solutions in lower-dimensional gauged supergravities and then uplifting to ten dimensions, yielding $Li_4 \times H_2$ in 6D leading to massive IIA and $Li_3 \times H_2$ in 5D leading to Type IIB. The main contributions are explicit, non-supersymmetric Lifshitz solutions for all $z \ge 1$, with flux quantization imposing relations between $z$ and the lower-dimensional couplings, and clear brane-intersection interpretations in ten dimensions. The findings provide concrete string-theoretic realizations of non-relativistic holographic geometries and lay groundwork for future studies of Lifshitz black holes and stability analyses.

Abstract

We derive Lifshitz configurations in string theory for general dynamical exponents z \geq 1. We begin by obtaining simple Li x Omega solutions to supergravities in diverse dimensions, with Omega a compact constant curvature manifold. Then we uplift the solutions to ten dimensions, providing configurations that correspond to warped compactifications in Type II string theory.