Integrability for the spectrum of Jordanian AdS/CFT

TL;DR

This paper investigates the integrability of the Jordanian deformed AdS/CFT spectrum, demonstrating that despite symmetry breaking, the spectrum remains solvable using Baxter methods, and matches string theory predictions at weak coupling.

Contribution

It shows that the spectrum of the Jordanian deformed AdS/CFT can be solved with Baxter techniques, even with broken highest-weight structures, and provides explicit analytic expressions matching string theory results.

Findings

Spectrum remains solvable via Baxter framework.

Analytic expressions match string spectrum at one-loop.

Results support the Jordanian AdS/CFT correspondence.

Abstract

Jordanian deformations offer rare integrable realisations of non-AdS holography, whose solvability methods differ from conventional AdS/CFT examples. Here we study the $\mathfrak{sl}(2,R)$ sector of the Jordanian deformed $AdS_5\times S^5$ string and its weak-coupling spin chain counterpart: the $\mathrm{XXX}_{-1/2}$ model with a non-abelian Jordanian Drinfel'd twist. While the twist breaks the usual highest-weight structure that underlies conventional Bethe ans\"atze, we show that the complete spectrum remains solvable within the Baxter framework. We argue that the functional form of the $TQ$-relation is unchanged, yet the structure of the $Q$-functions is nontrivially modified. This allows us to obtain analytic expressions at arbitrary spin chain length $J$, which match the deformed string spectrum at the one-loop level and to subleading order in the large-$J$ expansion, despite the severely reduced symmetry. Our results provide nontrivial tests of the Jordanian AdS/CFT correspondence and lay the groundwork for implementing the Separation of Variables program in non-abelian Drinfel'd-twisted models.