Protected states in $\mbox{AdS}_3$ backgrounds from integrability

TL;DR

This paper develops an algebraic Bethe Ansatz framework for string theory on specific AdS3 backgrounds, identifying protected states and their energies, and confirming these results with supergravity and orbifold spectrum calculations.

Contribution

It introduces the ABA for AdS3 string backgrounds and determines protected string wave functions and energies, extending understanding of protected spectra in these theories.

Findings

Protected string energies are invariant to all orders in α'

Wave functions of protected states are explicitly constructed

Results agree with supergravity and orbifold spectrum calculations

Abstract

We write down the Algebraic Bethe Ansatz for string theory on $\mbox{AdS}_3\times\mbox{S}^3\times\mbox{T}^4$ and $\mbox{AdS}_3\times\mbox{S}^3\times\mbox{K3}$ in its orbifold limits. We use it to determine the wave-functions of protected closed strings in these backgrounds and prove that their energies are protected to all orders in $\alpha'$. We further apply the ABA to find the wave functions of protected states of $\mbox{AdS}_3\times\mbox{S}^3\times\mbox{S}^3\times \mbox{S}^1$ and its $\mathbf{Z}_2$ orbifold. Our findings match with protected spectrum calculations from supergravity, $\mbox{Sym}^N$ orbifolds and apply to the complete moduli space of these theories, excluding orbifold blow-up modes for which further analysis is necessary.