Looking for (and not finding) a bulk brane

TL;DR

This paper investigates the conditions under which boundary conformal field theories (BCFTs) have consistent holographic duals with end-of-the-world branes, concluding such duals are rarely possible due to causal and spectral constraints.

Contribution

It introduces a framework for analyzing BCFT holography via Lorentzian correlators and demonstrates that bulk brane singularities impose restrictive, often non-generic, spectral conditions on BCFTs.

Findings

Bulk brane singularities constrain BCFT spectra.

Holographic duals with localized branes are almost never generic.

Causal structure imposes strong restrictions on BCFTs.

Abstract

When does a holographic CFT with a boundary added to it (a BCFT) also have a `good' holographic dual with a localized gravitating end-of-the-world brane? We argue that the answer to this question is almost never. By studying Lorentzian BCFT correlators, we characterize constraints imposed on a BCFT by the existence of a bulk causal structure. We argue that approximate `bulk brane' singularities place restrictive constraints on the spectrum of a BCFT that are not expected to be true generically. We discuss how similar constraints implied by bulk causality might apply in higher-dimensional holographic descriptions of BCFTs involving a degenerating internal space. We suggest (although do not prove) that even these higher-dimensional holographic duals are not generic.