Abstract
Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterising field theories with non-trivial dynamical critical exponent z ≠ 1 emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, toy models of generic corrections can lead (presumably as one possibility among many) to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent AdS 2 × R 2 geometry. Thus, at least in these cases, the Lifshitz scaling characterises the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects.
Highlights
JHEP02(2014)085 admissible [16], it is an open question in this case what the correct interpretation of the singularities is.1 The results of this note will not apply to the solutions, like those of [6], which have exact Lifshitz scaling symmetry
We show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, toy models of generic corrections can lead to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent AdS2 × R2 geometry. At least in these cases, the Lifshitz scaling characterises the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects
Asymptotically AdS extremal black branes whose near-horizon geometry is of the Lifshitz form were found in [17, 18] by studying the solutions of the theory with action
Summary
We find full solutions with AdS2 × R2 in the deep IR, a large Lifshitz scaling region along the flow to the UV, and asymptotically AdS4 boundary conditions. We add them with appropriate coefficients to generate a flow as one goes to larger values of r, and solve the equations using standard “shooting” techniques to hit AdS4. We will find that quite naturally, large Lifshitz scaling regions (matching onto the solutions of [17, 18]) appear along the flow. We begin by sketching the qualitative nature of the expected flow analytically
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