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

TL;DR

This paper constructs and analyzes boundary states for D-branes in Lorentzian AdS_3 using discrete series representations, ensuring unitarity, spectral flow symmetry, and revealing infinite BPS states in superstring backgrounds.

Contribution

It introduces a method to build consistent boundary states in Lorentzian AdS_3 with discrete series, maintaining unitarity and spectral flow symmetry, and explores their implications in superstring theory.

Findings

Constructed Cardy states compatible with unitarity and spectral flow.

Demonstrated the existence of infinite BPS states in superstring models.

Showed the brane interpretation of the boundary states.

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.