Holographic Quantum Critical Transport without Self-Duality

TL;DR

This paper extends the holographic description of 2+1d quantum critical transport by adding a controlled higher-derivative coupling of the bulk Maxwell field to the spacetime curvature via a Weyl term with coefficient $\gamma$. This breaks electromagnetic self-duality in AdS$_4$ and yields a nontrivial frequency dependence of the boundary conductivity $\sigma(\omega)$, while preserving a DC value $\sigma_0 = (1+4\gamma)/g_4^2$ and a high-frequency limit $\sigma(\infty)=1/g_4^2$. Causality and stability considerations impose $-1/12 \le \gamma \le 1/12$, and the bulk-boundary relations resemble particle-vortex duality through exact constraints like $K^T(\omega,q)\,\widehat{K}^L(\omega,q)=1$. The sign of $\gamma$ signals particle-like ($\gamma>0$) or vortex-like ($\gamma<0$) transport, with a simple mapping to the three-point function $\langle T JJ \rangle$ via $a_2=-24\gamma$. Overall, the work provides a controlled, finite-coupling holographic framework to study frequency-dependent transport at quantum criticality and clarifies how higher-derivative bulk terms constrain boundary dynamics.

Abstract

We describe general features of frequency-dependent charge transport near strongly interacting quantum critical points in 2+1 dimensions. The simplest description using the AdS/CFT correspondence leads to a self-dual Einstein-Maxwell theory on AdS_4, which fixes the conductivity at a frequency-independent self-dual value. We describe the general structure of higher-derivative corrections to the Einstein-Maxwell theory, and compute their implications for the frequency dependence of the quantum-critical conductivity. We show that physical consistency conditions on the higher-derivative terms allow only a limited frequency dependence in the conductivity. The frequency dependence is amenable to a physical interpretation using transport of either particle-like or vortex-like excitations.