On the IR completion of geometries with hyperscaling violation

TL;DR

This paper investigates how adding generic corrections to Einstein-Maxwell-dilaton gravity models can produce IR-complete solutions with an AdS_2 x R^2 region, connecting UV hyperscaling violating geometries to IR AdS_2 regions.

Contribution

It demonstrates the conditions under which IR-complete geometries with hyperscaling violation can emerge, including explicit numerical solutions and constraints on the theories.

Findings

Existence of IR-complete solutions with AdS_2 x R^2 in corrected models

Numerical flow from AdS_4 to AdS_2 x R^2 with intermediate hyperscaling and Lifshitz scaling

Constraints on Einstein-Maxwell-dilaton theories admitting such IR completions

Abstract

We study solutions to Einstein-Maxwell-dilaton gravity with a constant magnetic flux which describe, in the holographic AdS/CFT framework, field theories characterized by a dynamical critical exponent and a hyperscaling violation exponent. Such solutions are known to be IR-incomplete due to the presence of a running dilaton, which drives the theory towards strong coupling in the IR, where quantum corrections become important. After introducing generic corrections, in this note we examine the conditions for the emergence of an AdS_2 x R^2 region close to the horizon, which provides an IR-completion for the hyperscaling violating solutions. In the presence of these corrections, we construct explicit numerical solutions where the geometry flows from AdS_4 in the UV to AdS_2 x R^2 in the deep IR, with an intermediate region which exhbits both hyperscaling violation and Lifshitz scaling.We also provide constraints on the structure of Einstein-Maxwell-dilaton theories that admit such solutions, as well as an emergent AdS_2 x R^2 region in the infrared.