Looking at Shadows of Entanglement Wedges

Abstract

We present a new method of deriving shapes of entanglement wedges directly from CFT calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure, coincide perfectly with shadows of entanglement wedges in AdS/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher dimensional CFTs with a round ball subsystem. On the other hand if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large N factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally we study other distinguishability measures to define CFT wedges. We observe that some of measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT and we give a heuristic explanation for this. This paper is an extended version of our earlier letter arXiv:1908.09939 and includes various new observations and examples.