Entanglement R\'{e}nyi entropies in celestial holography

TL;DR

This paper explores the holographic duality between celestial conformal field theories and higher-dimensional spacetimes, calculating entanglement Rényi entropies using cosmic branes and revealing universal contributions related to conformal symmetry.

Contribution

It introduces a holographic framework for computing entanglement Rényi entropies in celestial CFTs via cosmic branes, connecting twist operators to bulk geometric objects.

Findings

Universal form of EREs dictated by conformal symmetry

Universal contribution vanishes for d=4 mod 4

Universal contribution proportional to cutoff in Planck units

Abstract

Celestial holography is the conjecture that scattering amplitudes in $(d+2)$-dimensional asymptotically Minkowski spacetimes are dual to correlators of a $d$-dimensional conformal field theory (CFT) on the celestial sphere, called the celestial CFT (CCFT). In a CFT, we can calculate sub-region entanglement R\'{e}nyi entropies (EREs), including entanglement entropy (EE), from correlators of twist operators, via the replica trick. We argue that CCFT twist operators are holographically dual to cosmic branes in the $(d+2)$-dimensional spacetime, and that their correlators are holographically dual to the $(d+2)$-dimensional partition function (the vacuum-to-vacuum scattering amplitude) in the presence of these cosmic branes. We hence compute the EREs of a spherical sub-region of the CCFT's conformal vacuum, finding the form dictated by conformal symmetry, including a universal contribution determined by the CCFT's sphere partition function (odd $d$) or Weyl anomaly (even $d$). We find that this universal contribution vanishes when $d=4$ mod $4$, and otherwise is proportional to $i$ times the $d^{\textrm{th}}$ power of the $(d+2)$-dimensional long-distance cutoff in Planck units.