Spatially modulated instabilities of holographic gauge-gravitational anomaly

TL;DR

This paper investigates perturbative instabilities in a holographic model with gauge and gravitational anomalies, revealing conditions for instability and implications for the reliability of the theory with a gravitational Chern-Simons term.

Contribution

It identifies two sources of instabilities in Einstein-Maxwell-Chern-Simons theory with gravitational anomaly, emphasizing the effects of mixed gauge-gravitational anomaly and the limitations of large Chern-Simons coupling.

Findings

Instability due to a real mass-squared below the BF bound in AdS2.

Existence of a singular momentum where unstable modes appear.

Theory becomes unreliable unless gravitational Chern-Simons coupling is small.

Abstract

We performed a study of the perturbative instabilities in Einstein-Maxwell-Chern-Simons theory with a gravitational Chern-Simons term, which is dual to a strongly coupled field theory with both chiral and mixed gauge-gravitational anomaly. With an analysis of the fluctuations in the near horizon regime at zero temperature, we found that there might be two possible sources of instabilities. The first one corresponds to a real mass-squared which is below the BF bound of AdS$_2$, and it leads to the bell-curve phase diagram at finite temperature. The effect of mixed gauge-gravitational anomaly is emphasised. Another source of instability is independent of gauge Chern-Simons coupling and exists for any finite gravitational Chern-Simons coupling. There is a singular momentum close to which unstable mode appears. The possible implications of this singular momentum are discussed. Our analysis suggests that the theory with a gravitational Chern-Simons term around Reissner-Nordstr\"om black hole is unreliable unless the gravitational Chern-Simons coupling is treated as a small perturbative parameter.