Boundary States of D-branes in AdS_3 Based on Discrete Series

TL;DR

The paper investigates boundary states for D-branes in AdS3 through the lens of the SL(2,R) WZW model, emphasizing open-closed duality on Lorentzian worldsheets and constructing Cardy boundary states from the discrete-series. It derives and analyzes the AdS2-brane spectrum, ensuring unitarity, normalizability, and spectral-flow invariance, and identifies a finite set of branes labeled by $L=0, obreak obreak obreak k-2$ corresponding to brane positions; in the open string sector it finds an infinite family of space-time 1/2-BPS chiral primaries consistent with spectral flow. The study shows that discrete-series boundary states interact only with short strings within the AdS radius, indicating a quantum truncation (fuzziness) of brane dynamics, while suggesting that continuous-series contributions are necessary to recover classical AdS2-brane physics and a complete AdS3/CFT2 boundary description. Overall, the work advances boundary CFT approaches to D-branes in AdS3 and lays a foundation for integrating continuous-series data to fully capture AdS2-brane geometry and dynamics.

Abstract

We study D-branes in the Lorentzian AdS_3 background from the viewpoint of boundary states, emphasizing the role of open-closed duality in string theory. Employing the world sheet with Lorentzian signature, we construct the Cardy states with the discrete series. We show that they are compatible with (1) unitarity and normalizability, and (2) the spectral flow symmetry, in the open string spectrum. We also discuss their brane interpretation. We further show that in the case of superstrings on AdS_3 x S^3 x T^4, our Cardy states yield an infinite number of physical BPS states in the open string channel, on which the spectral flows act consistently.