Hyperscaling violation : a unified frame for effective holographic theories

TL;DR

This paper classifies low-energy effective holographic theories with Lifshitz and Schrödinger symmetries using hyperscaling violation and dynamical exponents, revealing their parameter constraints and connections to microscopic string solutions.

Contribution

It provides a systematic classification of holographic theories based on hyperscaling violation and scaling exponents, linking them to string theory reductions and identifying universal features.

Findings

Classified theories constrained by null energy and specific heat conditions.

Identified universal emblackening factor for Lifshitz theories with one scale.

Connected classifications to microscopic string solutions and their scales.

Abstract

We investigate systematic classifications of low energy and lower dimensional effective holographic theories with Lifshitz and Schr\"odinger scaling symmetries only using metrics in terms of hyperscaling violation ($\theta$) and dynamical ($z$) exponents. Their consistent parameter spaces are constrained by null energy and positive specific heat conditions, whose validity is explicitly checked against a previously known result. From dimensional reductions of many microscopic string solutions, we observe the classifications are tied with the number of scales in the original microscopic theories. Conformal theories do not generate a nontrivial $\theta$ for a simple sphere reduction. Theories with Lifshitz scaling with one scale are completely fixed by $\theta$ and $z$, and have a universal emblackening factor at finite temperature. Dimensional reduction of intersecting M2-M5 requires, we call, spatial anisotropic exponents ($\sharp$), along with $z$=1, $\theta$=0, because of another scale. Theories with Schr\"odinger scaling show similar simple classifications at zero temperature, while require more care due to an additional parameter being a thermodynamic variable at finite temperature.