Protected states in AdS3backgrounds from integrability

Abstract

We write down the algebraic Bethe ansatz for string theory on AdS3 × S3 × T4 and AdS3 × S3 × K3 in its orbifold limits. We use it to determine the wavefunctions of protected closed strings in these backgrounds and prove that their energies are protected to all orders in α'. We further apply the ABA to find the wave functions of protected states of AdS3 × S3 × S3 × S1 and its Z2 orbifold. Our findings match with protected spectrum calculations from supergravity, SymN orbifolds and apply to the complete moduli space of these theories, excluding orbifold blow-up modes for which further analysis is necessary.