Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality

TL;DR

This paper investigates how a 5d Chern-Simons term affects holographic relative entropy and causality, revealing potential violations of positivity and causality constraints in the dual conformal field theory.

Contribution

It analyzes the impact of mixed gauge-gravity anomalies on relative entropy and causality within holography, highlighting potential violations at quadratic order in perturbations.

Findings

Mixed contributions to relative entropy can violate positivity.

Time-delay analysis suggests possible causality violations.

The problematic terms vanish at linear order in derivatives.

Abstract

In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor $T$ and current density $J$, there is a mixed contribution to the relative entropy bi-linear in $T$ and $J$, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.