Chiral anomalies and AdS/CMT in two dimensions

TL;DR

The paper analyzes holographic descriptions of finite-density 2d CFTs, showing that chiral anomalies completely determine boundary current correlators when the currents are not explicitly broken beyond the anomaly. It explains this via bulk Chern-Simons terms, explores the dual description with external currents (as in the D3/D3 system), and develops a holographic renormalization framework that reveals a novel Weyl anomaly associated with external currents. The work demonstrates that charged BTZ black holes in AdS$_3$ are modified mainly by a flat boundary connection, yielding consistent thermodynamics and a refined microscopic understanding of entropy. It discusses implications for AdS/CMT in two dimensions, indicating the need for deformations to access richer phases and nontrivial transport beyond linear response. The results collectively emphasize that in 2d holography, anomaly data largely governs the dynamics of currents and their observable consequences.

Abstract

I clarify some recent confusion regarding the holographic description of finite-density systems in two dimensions. Notably, the chiral anomaly for symmetry currents in 2d conformal field theories (CFT) completely determines their correlators. The important exception is a CFT with a gauge theory to which we may couple an external current, as in the probe D3/D3 system or the putative dual to the charged BTZ black hole. These systems are analyzed with an eye for potential condensed matter applications.