Looking for (and not finding) a bulk brane

TL;DR

The paper investigates when a BCFT with a boundary admits a good bulk dual featuring an end-of-the-world brane and argues this is generically unlikely. By analyzing Lorentzian BCFT two-point functions, it connects bulk causal structure to stringent, often non-generic, constraints on the BCFT spectrum and BOE data. The authors show that the proposed bulk ETW-brane description imposes a delicate alignment of boundary operator dimensions, which is not expected to be generic, and they explore more complex bulk geometries where this alignment is even less typical. They discuss top-down holographic BCFTs, causal depth, and potential extensions beyond ETW branes, highlighting that the existence of a simple bulk dual is not generic and may require fine-tuned boundary conditions or nonstandard bulk structures. The work thus questions the ubiquity of simple bulk branes in holographic BCFTs and outlines a framework to test bulk causality against BCFT data.

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.

Figures (16)

• Figure 1: (a) A light ray leaving the boundary and returning to the boundary at a later time (in this example reflecting off an ETW brane); (b) The bulk causal structure then implies new 'bulk brane' singularities in the BCFT to the future of a BCFT operator; (c) The bulk brane singularities require a careful alignment of operator dimensions appearing on the boundary of the BCFT.
• Figure 2: A BCFT on a half-plane $\mathbb{R}^{d-1} \times \mathbb{R}^+$. Here, $x_0$ and $\vec{x}$ are coordinates parallel to the boundary; $x_\perp$ is a coordinates perpendicular to the planar boundary, which sits at $x_\perp=0$.
• Figure 3: Pictorial representation of \ref{['eq:bcft_crossing']}. The thick line represents the boundary; thin lines represent fusion of external operators into bulk or boundary operators; dotted lines represent correlators.
• Figure 4: Our simple model in which the bulk is locally AdS$_{d+1}$, but is terminated by an ETW brane. We depict here the AdS$_d$ foliation of AdS$_{d+1}$.
• Figure 5: We depict various regions of the Lorentzian interval for a BCFT in terms of various cross-ratios. Importantly we note that the causal diamond bounded by the lightcone of the operator $\mathcal{O}(x)$ and its reflection off the boundary is described by the radial cross-ratio $\rho$ living on the unit circle. It interpolates between the initial lightcone at $\rho = e^{i 0}$ and the reflected ligthcone at $\rho = e^{i \pi}$.

Theorems & Definitions (1)

• Conjecture 1