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D-branes in an AdS_3 background

Sonia Stanciu

TL;DR

This work analyzes D-brane configurations in AdS$_3\times S^3\times T^4$ with a NS-NS $B$-field using an exact WZW/SCFT framework and boundary-state formalism. It identifies two conformally invariant gluing classes, type-N and type-D, and systematically derives their geometric realizations: type-D yields branes along shifted conjugacy classes while type-N branes generally wrap open submanifolds or cosets and do not preserve the bulk current algebra. The study extends to an $N=1$ supersymmetric extension, showing that a consistent superconformal structure exists for type-D configurations, and computes spacetime supersymmetry, finding that these SUSY-preserving branes are BPS with half of the background supersymmetry preserved. The results illuminate the microscopic D-brane content in AdS backgrounds, connect to sigma-model perspectives, and point to duality structures such as Poisson–Lie T-duality, with implications for holographic setups and D-brane dynamics in NS-NS flux backgrounds.

Abstract

We study the possible D-brane configurations in an AdS_3 x S^3 x T^4 background with a NS-NS B field. We use its WZW model description and the boundary state formalism, and we analyze the bosonic and the N=1 supersymmetric cases separately. We also discuss the corresponding classical open string sigma model. We determine the spacetime supersymmetry preserved by the supersymmetric D-brane configurations.

D-branes in an AdS_3 background

TL;DR

This work analyzes D-brane configurations in AdS with a NS-NS -field using an exact WZW/SCFT framework and boundary-state formalism. It identifies two conformally invariant gluing classes, type-N and type-D, and systematically derives their geometric realizations: type-D yields branes along shifted conjugacy classes while type-N branes generally wrap open submanifolds or cosets and do not preserve the bulk current algebra. The study extends to an supersymmetric extension, showing that a consistent superconformal structure exists for type-D configurations, and computes spacetime supersymmetry, finding that these SUSY-preserving branes are BPS with half of the background supersymmetry preserved. The results illuminate the microscopic D-brane content in AdS backgrounds, connect to sigma-model perspectives, and point to duality structures such as Poisson–Lie T-duality, with implications for holographic setups and D-brane dynamics in NS-NS flux backgrounds.

Abstract

We study the possible D-brane configurations in an AdS_3 x S^3 x T^4 background with a NS-NS B field. We use its WZW model description and the boundary state formalism, and we analyze the bosonic and the N=1 supersymmetric cases separately. We also discuss the corresponding classical open string sigma model. We determine the spacetime supersymmetry preserved by the supersymmetric D-brane configurations.

Paper Structure

This paper contains 17 sections, 105 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. The bosonic $\text{AdS}_3\times S^3\times T^4$ background
  3. Boundary states
  4. D-brane solutions and geometry
  5. Relation to the sigma model approach
  6. The $\mathrm{SL}(2,\mathbb R)$ component
  7. The $\mathrm{SU}(2)$ component
  8. The $N{=}1$ supersymmetric extension
  9. Spacetime supersymmetry
  10. Discussion
  11. Conjugacy classes of $\mathrm{SL}(2,\mathbb R)$
  12. Jordan normal forms
  13. The geometry of the conjugacy classes
  14. The causal structure of the conjugacy classes
  15. $\EuScript{C}_{\pm\pm}$
  16. ...and 2 more sections

Figures (1)

  • Figure 1: The different types of conjugacy classes of $\mathrm{SL}(2,\mathbb R)$.