Boundary States for D-branes in $AdS_3$

TL;DR

This work constructs boundary states for D-branes in $AdS_3$ by wrapping twisted conjugacy classes of ${\rm SL}(2,\mathbb{R})$, showing these branes couple only to continuous representations and satisfy Cardy consistency. The authors regularize divergences in boundary-state overlaps, derive a boundary state localized on the conjugacy class via $|B\rangle \propto \sum_s e^{-is\psi_0}|I^s\rangle$, and demonstrate that the resulting open-string spectrum is universal across all branes. They connect the CFT construction to the geometric brane picture, discuss winding sectors and spectral flow, and argue the boundary state is exact at finite level $k$, with $1/k$ corrections manifesting only as overall renormalizations. The results align with open-string quantization in prior work and provide a coherent, consistent description of D-branes in $AdS_3$ with implications for long-string sectors and holographic setups.”

Abstract

We construct boundary states representing D-strings in $AdS_3$. These wrap twisted conjugacy classes of SL(2,R), and the boundary states are therefore based on continuous representations only. We check Cardy's condition and find a consistent open string spectrum. The open string spectrum on all the D-branes is the same.