Semi-local quantum criticality in string/M-theory

Abstract

Semi-local quantum critical behaviour in D − 1 spacetime dimensions can be holographically described by metrics that are conformal to $Ad{S_2}\times {{\mathbb{R}}^{D-2 }}$, with the conformal factor characterised by a parameter η. We analyse such “η-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 η = 1 geometry in the IR. Adding a fourth charge provides a mechanism to resolve the singularity of the η-geometry, replacing it with an $Ad{S_2}\times {{\mathbb{R}}^2}$ factor in the IR, while maintaining a large region where the η-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 η-geometries, with various values of η, can be obtained from the dimensional reduction of geometries consisting of AdS or Lifshitz geometries with flat directions.