Boundary States for AdS_2 Branes in AdS_3

TL;DR

The authors construct boundary states for $AdS_2$ branes in $AdS_3$ within the $SL(2,\mathbb{R})$ WZW framework, employing a new ansatz for disk one-point functions and a degenerate-field analysis to derive a family of solutions parametrized by $\Theta$. In the semiclassical limit, these boundary states reproduce the $AdS_2$ brane geometry with the brane located at $\psi=\Theta$ in $AdS_2$ coordinates, and the identity overlap matches the Born-Infeld action. They compute annulus amplitudes and obtain the open-string spectral density for strings stretched between branes, finding a $\Theta$-dependent density that diverges due to the branes’ noncompact volume, while the $\Theta_1=\Theta_2$ case removes this dependence. At finite temperature, the boundary-state construction yields a thermal free-energy result in agreement with prior open-string computations, reinforcing the validity of the boundary-state approach for non-rational CFTs in AdS backgrounds and enabling further holographic explorations beyond supergravity.

Abstract

We construct boundary states for the AdS_2 D-branes in AdS_3. We show that, in the semi-classical limit, the boundary states correctly reproduce geometric configurations of these branes. We use the boundary states to compute the one loop free energy of open string stretched between the branes. The result agrees precisely with the open string computation in hep-th/0106129.