Density versus chemical potential in holographic field theories

TL;DR

This paper investigates the relationship between charge density and chemical potential in various holographic field theories, revealing power-law behaviors and thermodynamic constraints across different models.

Contribution

It provides a comparative analysis of charge density versus chemical potential in diverse holographic models, identifying universal power-law behaviors and thermodynamic bounds.

Findings

Charge density scales as a power law with chemical potential.

The power-law exponent varies across models but is constrained by thermodynamics.

Most models satisfy the condition that the exponent is greater than or equal to one.

Abstract

We study the relationship between charge density ({\rho}) and chemical potential ({\mu}) for an array of Lorentz invariant 3 + 1 dimensional holographic field theories with the minimal structure of a conserved charge. The systems considered include Dp-Dq probe brane constructions and probe and backreacted 'bottom-up' models with gauge and scalar fields. In all cases, at large density, the relationship is well modelled by a power law behaviour of the form {\rho} $\propto$ {\mu}^{\alpha}. A variety of powers {\alpha} are found in the brane systems while in most of the bottom-up models {\alpha} is determined by the underlying conformal symmetry. Further, it is demonstrated that basic thermodynamical and causality constraints demand {\alpha} \geq 1, a condition that was realized in each system considered.