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 contributionto 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.
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Bhattacharyya, A., Cheng, L. & Hung, LY. Relative entropy, mixed gauge-gravitational anomaly and causality. J. High Energ. Phys. 2016, 121 (2016). https://doi.org/10.1007/JHEP07(2016)121
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DOI: https://doi.org/10.1007/JHEP07(2016)121