D-Branes in $\textbf{AdS}_3\times \textbf{S}^3 \times \textbf{S}^3 \times \textbf{S}^1$

TL;DR

This work analyzes spherical and AdS$_2$ D-branes in the NS-NS flux background $AdS_3$×$S^3$×$S^3$×$S^1$, proposed to be dual to the symmetric orbifold of eight free fermions and two bosons. Using the NS-R worldsheet description at $k_+=k_-=2$, it constructs spherical-brane boundary states via Ishibashi states in all spectrally flowed sectors, computes cylinder amplitudes, and translates them into open-string channels. It then develops the dual CFT dictionary by building maximally fractional boundary states in the seed theory and in the symmetric orbifold, and shows that the worldsheet and CFT calculations match in the single-particle sector for both closed and open strings; AdS$_2$ branes are shown to correspond to interfaces in the symmetric orbifold. Overall, the paper provides a concrete consistency check of the AdS$_3$/CFT$_2$ duality in a NS-R framework and clarifies how boundary degrees of freedom map across the dual descriptions, including implications for tensionless-string-like regimes and interface physics.

Abstract

String theory on $\mathrm{ AdS}_3\times \mathrm{ S}^3 \times \mathrm{ S}^3 \times \mathrm{S}^1$ with two units of NS flux through each of the two $3$-spheres (and one unit of NS flux supporting the $\mathrm{AdS}_3$ factor) was recently argued to be exactly dual to the symmetric orbifold of eight free fermions and two bosons. This setup is interesting since it allows for a simple NS-R description. In this paper we study the spherical D-branes of this theory, and identify them with branes in the dual symmetric orbifold theory. We also comment briefly on the $\mathrm{ AdS}_2$ branes.