# Protected string spectrum in AdS3/CFT2 from worldsheet integrability

## TL;DR

This paper derives the protected string spectra in AdS3/CFT2 dual pairs using integrability and Bethe equations, revealing detailed spectral matches and discrepancies with supergravity predictions.

## Contribution

It provides the all-loop Bethe equations for protected spectra in AdS3/CFT2 and analyzes their representation as spin chains with length-changing interactions.

## Key findings

- Protected spectra match dual CFT2 and supergravity in AdS3 x S3 x T4.
- Fewer protected states are found in AdS3 x S3 x S3 x S1 than previous supergravity estimates.
- Protected states have equal su(2) charges on both S3 spheres.

## Abstract

We derive the protected closed-string spectra of AdS3/CFT2 dual pairs with 16 supercharges at arbitrary values of the string tension and of the three-form fluxes. These follow immediately from the all-loop Bethe equations for the spectra of the integrable worldsheet theories. Further, representing the underlying integrable systems as spin chains, we find that their dynamics involves length-changing interactions and that protected states correspond to gapless excitations above the Berenstein-Maldacena-Nastase vacuum. In the case of AdS3 x S3 x T4 the degeneracies of such operators precisely match those of the dual CFT2 and the supergravity spectrum. On the other hand, we find that for AdS3 x S3 x S3 x S1 there are fewer protected states than previous supergravity calculations had suggested. In particular, protected states have the same su(2) charge with respect to the two three-spheres.