AdS_2 D-Branes in Lorentzian AdS_3

TL;DR

This paper constructs and analyzes boundary states for AdS_2 D-branes in Lorentzian AdS_3, demonstrating their algebraic definition, boundary conditions, and the specific string states that couple to these branes.

Contribution

It provides a detailed free field formalism construction of AdS_2 D-branes in Lorentzian AdS_3, including boundary states and the identification of coupled string representations.

Findings

Only principal continuous series states couple to AdS_2 D-branes.

Boundary states satisfy twisted Dirichlet conditions.

Explicit form of boundary states derived using free field formalism.

Abstract

The boundary states for AdS_2 D-branes in Lorentzian AdS_3 space-time are presented. AdS_2 D-branes are algebraically defined by twisted Dirichlet boundary conditions and are located on twisted conjugacy classes of SL(2,R). Using free field representation of symmetry currents in the SL(2,R) WZNW model, the twisted Dirichlet gluing conditions among currents are translated to matching conditions among free fields and then to boundary conditions among the modes of free fields. The Ishibashi states are written as coherent states on AdS_3 in the free field formalism and it is shown that twisted Dirichlet boundary conditions are satisfied on them. The tree-level amplitude of propagation of closed strings between two AdS_2 D-branes is evaluated and by comparing which to the characters of sl(2,R) Kac-Moody algebra it is shown that only states in the principal continuous series representation of sl(2,R) Kac-Moody algebra contributes to the amplitude and thus they are the only ones that couple to AdS_2 D-branes. The form of the character of sl(2,R) principal continuous series and the boundary condition among the zero modes are used to determine the physical boundary states for AdS_2 D-branes.