Some remarks on D-branes in AdS_3

TL;DR

Parnachev and Sahakyan connect the algebraic boundary states of the $SL(2,\mathbb{R})$ WZNW model for $AdS_3$ with target-space D-branes wrapped on conjugacy classes. Through semiclassical overlaps and disk partition sums, they show boundary states implement branes on $H_3^+$ conjugacy classes and that the disk partition function reproduces the spacetime DBI action, including proper treatment of volume divergences. They classify D-branes into discrete and extended families, with discrete branes arising from degenerate representations via spectral flow and extended branes labeled by a complex parameter $\Theta$ mapping to $AdS_2$, $H_2$, or $dS_2$ branes after Wick rotation. The work provides a coherent CFT-to-geometry dictionary for D-branes in $AdS_3$, and highlights open questions about degenerate-representation branes and parafermionic structures in the $SL(2,\mathbb{R})/U(1)$ context.

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).