Comments on D-branes in AdS_3

TL;DR

This paper classifies and analyzes D-branes in AdS_3 that preserve a diagonal SL(2) symmetry, exploring their representations, boundary conditions, and implications for the AdS/CFT correspondence.

Contribution

It identifies three classes of D-branes in AdS_3 based on SL(2) representations and solves bootstrap equations for their wave functions, advancing understanding of boundary conditions in string theory.

Findings

Three classes of D-branes identified: degenerate, principal continuous, and principal discrete series.

Bootstrap equations solved for vacuum wave functions of these D-branes.

Discussion of the geometric interpretation and boundary conditions in the AdS/CFT context.

Abstract

We study D-branes that preserve a diagonal SL(2) affine Lie algebra in string theory on AdS_3. We find three classes of solutions, corresponding to the following representations of SL(2): (1) degenerate, finite dimensional representations with half integer spin, (2) principal continuous series, (3) principal discrete series. We solve the bootstrap equations for the vacuum wave functions and discuss the corresponding open string spectrum. We argue that from the point of view of the AdS/CFT correspondence, the above D-branes introduce boundaries with conformal boundary conditions into the two dimensional spacetime. Open string vertex operators correspond to boundary perturbations. We also comment on the geometric interpretation of the branes.