Semi-local quantum criticality in string/M-theory

TL;DR

This paper explores semi-local quantum critical geometries in string/M-theory, showing how they can be realized as solutions in supergravity, and how additional charges can resolve singularities, connecting these geometries to higher-dimensional models.

Contribution

It provides a top-down supergravity construction of $ ext{eta}$-geometries, demonstrating their emergence from known $AdS$ and Lifshitz solutions and analyzing charge configurations that resolve IR singularities.

Findings

$ ext{eta}$-geometries can be embedded in supergravity models.

Adding a fourth charge resolves IR singularities.

Various $ ext{eta}$-geometries derive from dimensional reduction of higher-dimensional solutions.

Abstract

Semi-local quantum critical behaviour in $D-1$ spacetime dimensions can be holographically described by metrics that are conformal to $AdS_2\times\mathbb{R}^{D-2}$, with the conformal factor characterised by a parameter $\eta$. We analyse such "$\eta$-geometries" in a top-down setting by focussing on the $U(1)^4$ truncation of D=4 N=8 gauged supergravity. The model has extremal black hole solutions carrying three non-zero electric or magnetic charges which approach $AdS_4$ in the UV and an $\eta=1$ geometry in the IR. Adding a fourth charge provides a mechanism to resolve the singularity of the $\eta$-geometry, replacing it with an $AdS_2\times\mathbb{R}^2$ factor in the IR, while maintaining a large region where the $\eta$-geometry scaling is approximately valid. Some of the magnetically charged black hole solutions preserve supersymmetry while others just preserve it in the IR. Finally, we show that $\eta$-geometries, with various values of $\eta$, can be obtained from the dimensional reduction of geometries consisting of $AdS$ or Lifshitz geometries with flat directions.