Generalized Holographic Quantum Criticality at Finite Density

TL;DR

The paper provides a unifying framework for generalized holographic quantum criticality at finite density by showing that near-extremal Einstein-Maxwell-Dilaton solutions can be understood as dimensional uplifts of higher-dimensional AdS/Lifshitz theories. Through generalized dimensional reduction, the authors connect IR scaling geometries to Lifshitz, Schrödinger, and AdS2-type limits, and they map the (γ,δ) parameter space to distinct IR universality classes with calculable transport and thermodynamic scalings. This construction also resolves naked singularities via Kaluza-Klein effects and offers UV completions for the IR EFT, yielding a network of uplift relations across numerous higher-dimensional theories. The results provide practical tools for computing IR transport (DC/AC) and thermodynamics and suggest broad applicability to various rotating branes and AdS dilatonic black holes. Overall, the work positions near-extremal EMD geometries as the most general holographic quantum critical IR states at finite density and links them to concrete higher-dimensional embeddings.

Abstract

We show that the near-extremal solutions of Einstein-Maxwell-Dilaton theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions. This explains the scaling of their thermodynamic functions and their IR transport coefficients, the nature of their spectra, the Gubser bound, and regulates their singularities. We propose that these are the most general quantum critical IR asymptotics at finite density of EMD theories.