Black Hole Interior Operators and Dilatation Symmetry in Planar Black Branes

TL;DR

This paper demonstrates that the boundary representation of black hole interior modes in planar AdS black branes respects the bulk's dilatation symmetry, confirming the covariance of the Papadodimas-Raju reconstruction.

Contribution

It derives a covariance condition for boundary interior mode representations and shows that Papadodimas-Raju mirror operators satisfy this condition, inheriting the scaling symmetry.

Findings

Boundary representations of interior modes transform covariantly under boundary dilatations.

Papadodimas-Raju mirror operators satisfy the derived covariance condition.

The bulk's scaling symmetry is inherited by the boundary reconstruction.

Abstract

Planar AdS black branes have a scaling symmetry that maps a brane solution at one temperature to a solution at another. It is natural to expect that boundary representations of bulk field modes should inherit this symmetry i.e. their correlators should transform covariantly under boundary dilatations. We derive a covariance condition that any boundary representation of interior modes in a planar AdS black brane should satisfy. We then show that Papadodimas-Raju mirror operators satisfy this condition. Thus the Papadodimas-Raju reconstruction of the bulk interior, although state-dependent, inherits the scaling symmetry of planar AdS black holes.