Lifshitz Solutions of D=10 and D=11 supergravity

TL;DR

Donos and Gauntlett construct infinite families of Lifshitz solutions with z=2 in D=10/11 supergravity by using cones over five- and seven-dimensional Einstein manifolds, yielding Lif$_4$($z=2$) and Lif$_3$($z=2$) duals in 1+2 and 1+1 dimensions. The solutions are connected across type IIB, type IIA, and M-theory via T-duality and uplifting, and Sasaki–Einstein internal spaces can preserve supersymmetry when fluxes satisfy (1,1) primitive or (0,2) conditions. They provide explicit realizations on T^{1,1} and Y^{p,q}, as well as Lif$_3$ constructions from E$_7$, with flux data encoded by a harmonic two-form W, a function f, and a flux g. This work expands the top-down landscape of holographic Lifshitz geometries, avoids previous no-go results through general flux configurations, and points to potential condensed-matter applications including black holes and RG flows linking Schrödinger, Lifshitz, and AdS regimes.

Abstract

We construct infinite families of Lifshitz solutions of D=10 and D=11 supergravity with dynamical exponent z=2. The new solutions are based on five- and seven-dimensional Einstein manifolds and are dual to theories in 1+2 and 1+1 spacetime dimensions, respectively. When the Einstein spaces are Sasaki-Einstein, the solutions are supersymmetric.

Figures (1)

• Figure 1: Numerical solutions for the function $\bar{f}(y)$ for $(p,q)$= $(4,1)$ (i.e. $a\sim 0.10$) - dark blue; $(3,1)$ (i.e. $a\sim 0.18$) - green; $(2,1)$ (i.e. $a\sim 0.39$) - red; $(3,2)$ (i.e. $a\sim 0.64$) - cyan. For each case we have plotted $\bar{f}$ just for the values $y\in[y_1,y_2]$.