Tensionless strings on AdS$_3$ $\times$ S$^3$ $\times$ S$^3$ $\times$ S$^1$

Abstract

We propose that string theory on AdS$_3$ $\times$ S$^3$ $\times$ S$^3$ $\times$ S$^1$ with two units of NS-NS flux through each of the two 3-spheres is exactly dual to the symmetric orbifold of 2 bosons and 8 free fermions. Here, one of the two bosons describes the compact S$^1$, while the other one corresponds to the radial (non-compact) direction of AdS$_3$. Unlike the analogous situation for AdS$_3$ $\times$ S$^3$ $\times$ $\mathbb{T}$$^4$, the description makes sense both in the NS-R as well as the hybrid formulation, and we explain the duality in both frameworks.