Some comments on Anti-de Sitter D-branes

TL;DR

The article investigates ${\rm AdS}_2\times {\rm S}^2$ D3-branes in ${\rm AdS}_3\times {\rm S}^3$ by (i) computing quadratic DBI fluctuations around semi-classical brane configurations and comparing with a CFT framework, (ii) analyzing open-string states via a worldsheet CFT and identifying their representation content, and (iii) exploring classical open-string dynamics and spectral flow on these branes. The semi-classical fluctuation spectrum forms discrete $SU_2(\mathbb{C})\times SL_2(\mathbb{R})$ representations largely independent of brane charges, and shows partial agreement with CFT predictions, highlighting the need for full Cardy-boundary-state data to complete the open-string spectrum. Open-string dynamics reveal a partial preservation of spectral flow, and in the neutral, straight-brane case there is a compelling argument that the open-string sector is half of the closed-string spectrum due to a reflection symmetry. Overall, the work clarifies how DBI fluctuations and CFT approaches constrain the open-string spectrum on AdS-branes and points toward the boundary-state data required for a complete match.

Abstract

We present some preliminary investigations about the AdS2*S2 D3-branes in AdS3*S3. We analyse the quadratic fluctuations of Dirac-Born-Infeld action around a given semi-classical D-brane configuration and compare them with results obtained by using conformal field theory techniques. We finally study classical motions of open strings attached to those D-branes and analyse the role of the spectral flow in this context.