Asymptotic Bethe Ansatz from String Sigma Model on S^3 x R

TL;DR

The paper demonstrates that the asymptotic string Bethe ansatz (AFS equations) for the S^3×R sector of AdS5×S5 can be derived from an underlying inhomogeneous dynamical spin chain (IDSC) model. By analyzing the continuous limit and integrating out the $\theta$-degrees of freedom, the authors show that AFS emerges as an effective description at large coupling and length, with energy and momentum encoded in a resolvent formalism and magnon Zhukovsky variables. The work links gauge/string theory data across BMN, large-$\lambda$, and finite-gap regimes and highlights the potential of IDSC to reconcile perturbative SYM results with semiclassical string theory, while outlining avenues to generalize to the full superstring. It also elucidates the periodicity of worldsheet momentum and the role of the dressing phase within this integrable framework.

Abstract

We derive the asymptotic Bethe ansatz (AFS equations) for the string on S^3 x R sector of AdS_5 x S^5 from the integrable nonhomogeneous dynamical spin chain for the string sigma model proposed in GKSV. It is clear from the derivation that AFS equations can be viewed only as an effective model describing a certain regime of a more fundamental inhomogeneous spin chain.