Some remarks on D-branes in AdS_3

TL;DR

This paper explores the relationship between algebraic boundary states and geometric D-branes in AdS_3, confirming their consistency and linking string partition functions to the DBI action.

Contribution

It demonstrates the equivalence of algebraic and target space descriptions of D-branes in AdS_3 and analyzes the role of spectral flow symmetry in their construction.

Findings

Boundary states correspond to D-branes wrapping conjugacy classes in AdS_3.

Disk partition function reproduces the spacetime DBI action.

Spectral flow symmetry is crucial for constructing certain D-branes.

Abstract

We investigate the relation between the algebraic construction of boundary states in AdS_3 and the target space analysis of D-branes and show the consistency of the two descriptions. We compute, in the semiclassical regime, the overlap of a localized closed string state with boundary states and identify the latter with D-branes wrapping conjugacy classes in AdS_3. The string partition function on the disk is shown to reproduce the spacetime DBI action. Other consistency checks are performed. We also comment on the role of the spectral flow symmetry of the underlying SL(2,R)/U(1) coset model in constructing D-branes that correspond to degenerate representations of SL(2,R).