Spectrum of End of the World Branes in Holographic BCFTs

TL;DR

This paper investigates the overlaps between boundary states in conformal field theories and their gravity duals, revealing that such overlaps are exponentially suppressed and relate to black hole microstates, with results extending to higher dimensions.

Contribution

It provides a gravity dual analysis of boundary state overlaps in holographic BCFTs, connecting them to black hole microstates and extending the analysis beyond two dimensions.

Findings

Overlap between different boundary states is exponentially suppressed.

Holographic boundary states are akin to random vectors among black hole microstates.

The suppression factor depends on brane tensions in higher dimensions.

Abstract

We study overlaps between two regularized boundary states in conformal field theories. Regularized boundary states are dual to end of the world branes in an AdS black hole via the AdS/BCFT. Thus they can be regarded as microstates of a single sided black hole. Owing to the open-closed duality, such an overlap between two different regularized boundary states is exponentially suppressed as $\langle \psi_{a} | \psi_{b} \rangle \sim e^{-O(h^{(min)}_{ab})}$, where $h^{(min)}_{ab}$ is the lowest energy of open strings which connect two different boundaries $a$ and $b$. Our gravity dual analysis leads to $h^{(min)}_{ab} = c/24$ for a pure AdS$_3$ gravity. This shows that a holographic boundary state is a random vector among all left-right symmetric states, whose number is given by a square root of the number of all black hole microstates. We also perform a similar computation in higher dimensions, and find that $h^{( min)}_{ab}$ depends on the tensions of the branes. In our analysis of holographic boundary states, the off diagonal elements of the inner products can be computed directly from on-shell gravity actions, as opposed to earlier calculations of inner products of microstates in two dimensional gravity.