Universal conductivity and central charges

TL;DR

The paper identifies a universality class of conformal field theories in spacetime dimensions $d>2$ whose thermodynamics and transport coefficients are fixed by central charges via holographic (AdS) duals. It shows that the pressure and charge susceptibility scale with temperature as $P(T)=c'T^{d}$ and $\chi(T)=k'T^{d-2}$, with explicit ratios for $c'/c$ and $k'/k$, and that the dc conductivity satisfies $\frac{\sigma}{\chi}=\frac{1}{4\pi T}\frac{d}{d-2}$, mirroring the celebrated $\eta/s=1/4\pi$ bound. In $1+1$ dimensions, a distinct lack of hydrodynamics leads to $\chi = k/(2\pi)$ and $\sigma(\omega)=\frac{k}{2}\delta(\omega)$, while in holographic theories the conductivity is tightly controlled by thermodynamics through the dual gravity description. The work also discusses potential bound-like constraints on conductivity, compares holographic results to large-N models such as the $O(N)$ model, and outlines broader universality classes beyond gravity duals, emphasizing the role of large-N equivalences in determining universal transport properties.

Abstract

We discuss a class of critical models in d>1+1 dimensions whose electrical conductivity and charge susceptibility are fixed by the central charge in a universal manner. We comment on possible bounds on conductivity, as suggested by holographic duality.