Protected string spectrum in AdS3/CFT2 from worldsheet integrability

TL;DR

This work uses worldsheet integrability to derive the protected closed-string spectra of AdS3/CFT2 systems with 16 supercharges at arbitrary string tension and flux. By solving all-loop Bethe equations and implementing a spin-chain interpretation, the authors identify zero-momentum Bethe roots as the key carriers of protected states, with massless excitations generating a 2^{N0} degeneracy. For AdS3×S3×T4, the protected spectrum precisely matches the dual CFT2 and supergravity, while for AdS3×S3×S3×S1 the degeneracy is smaller than some supergravity expectations, enforcing J+ = J- for protected multiplets. Wrapping corrections cancel for these states, signaling a robust protected sector and suggesting a close relation to symmetric-product orbifold data; mixed-flux backgrounds preserve the same protected structure, highlighting the resilience of integrability-based predictions across moduli space.

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.

Figures (2)

• Figure 1: Two Dynkin diagrams for $\mathrm{psu}(1,1|2)$ with the simple roots indicated.
• Figure 2: A generic $\mathrm{psu}(1,1|2)$ representation $[h,j]_b$ contains sixteen irreducible $\mathrm{su}(1,1) \oplus \mathrm{su}(2)$ submodules, which are here represented by their charges under $\mathrm{su}(1,1) \oplus \mathrm{su}(2)$ and under $\mathrm{su}(2)_{\bullet}$. In this figure the charges of these submodules are depicted together with their eigenvalues under $\mathbf{J}_{\bullet}$. The solid red (blue) arrows indicate the action of the generators $\mathbf{Q}_1$ ($\dot{\mathbf{Q}}^2$) and the dashed red (blue) arrows indicate the action of generators $\mathbf{Q}_2$ ($\dot{\mathbf{Q}}^1$). Note that not all such actions are depicted. For $h=j$ the representation $(j,j)_b$ becomes reducible and splits into four short representations with highest weight states corresponding to the states in the double boxes.