Holographic R\'enyi relative divergence in JT gravity

TL;DR

This paper calculates the holographic Rnyi relative divergence between two states in JT gravity, revealing a non-perturbative result that relates to black hole geometries and background field changes.

Contribution

It provides the first non-perturbative holographic computation of Rnyi relative divergence in JT gravity for arbitrary source differences.

Findings

Divergence computed for large source differences yields a black hole with maximal temperature.

Analytic expression involves on-shell action of back-reacted black hole.

Discontinuous background field change contributes to the divergence.

Abstract

We holographically compute the R\'enyi relative divergence $D_{\alpha} (\rho_{+} || \rho_{-})$ between two density matrices $\rho_{+}, \; \rho_{-}$ prepared by path integrals with constant background fields $\lambda_{\pm}$ coupled to a marginal operator in JT gravity. Our calculation is non perturbative in the difference between two sources $ \lambda_{+} -\lambda_{-}$. When this difference is large, the bulk geometry becomes a black hole with the maximal temperature allowed by the R\'enyi index $\alpha$. In this limit, we find an analytic expression of the R\'enyi relative divergence, which is given by the on shell action of the back reacted black hole plus the contribution coming from the discontinuous change of the background field.