Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality

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.

21 pages, Details added, typos fixed, references updated; version to appear in JHEP

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Cited by in corpus (4)

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• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• Spatially modulated instabilities of holographic gauge-gravitational anomaly