Branes in the Euclidean AdS_3

TL;DR

This paper provides an exact microscopic description of maximally symmetric branes in Euclidean AdS_3, including explicit formulas for boundary states and spectral densities, with consistency checks and implications for D-branes in black hole geometries.

Contribution

It offers explicit formulas for boundary states and spectral densities of branes in Euclidean AdS_3, with detailed consistency checks and geometric comparisons.

Findings

Explicit boundary state formulas for Euclidean AdS_3 branes

Spectral density derived from reflection amplitude and boundary states

Consistency verified through Cardy condition and geometric analysis

Abstract

In this work we propose an exact microscopic description of maximally symmetric branes in a Euclidean $AdS_3$ background. As shown by Bachas and Petropoulos, the most important such branes are localized along a Euclidean $AdS_2 \subset AdS_3$. We provide explicit formulas for the coupling of closed strings to such branes (boundary states) and for the spectral density of open strings. The latter is computed in two different ways first in terms of the open string reflection amplitude and then also from the boundary states by world-sheet duality. This gives rise to an important Cardy type consistency check. All the results are compared in detail with the geometrical picture. We also discuss a second class of branes with spherical symmetry and finally comment on some implications for D-branes in a 2D back hole geometry.