Integrability for the spectrum of Jordanian AdS/CFT

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 $Ad{S}_5\times S^5$ 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 ansätze, 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.

v2: published version, added small clarifications; 45 pages, 1 table, 2 figures