Dispersing quasinormal modes in (2+1)-dimensional conformal field theories

Abstract

We study the charge response of conformal field theories (CFTs) at nonzero temperature in 2+1 dimensions using the anti-de Sitter (AdS)/CFT correspondence. A central role is played by the quasinormal modes (QNMs), specifically, the poles and zeros of the current correlators. We generalize our recent study of the QNMs of the ac charge conductivity to include momentum dependence. This sheds light on the various excitations in the CFT. We begin by discussing the $R$-current correlators of the $\mathcal{N}=8$ SU$({N}_{c})$ super-Yang-Mills theory at its conformal fixed point using holography. For instance, transitions in the QNM spectrum as a function of momentum clearly identify ``hydrodynamic-to-relativistic'' crossovers. We then extend our study to include four-derivative terms in the gravitational description allowing us to study more generic charge response as well as the role of the S duality, which plays a central role in understanding the correlators. The presence of special purely damped QNMs can lead to new behavior, distinct from what occurs in the aforementioned gauge theory. We also extend previous conductivity sum rules to finite momentum and discuss their interpretation in the gravity picture. A comparison is finally made with the conformal fixed point of the vector O($N$) model in the large-$N$ limit.