Jordanian spin chains for twisted strings in $AdS_5\times S^5$

TL;DR

This paper explores Jordanian deformations of the $AdS_5\times S^5$ superstring via integrable spin chains, developing a framework for twisted models, analyzing their spectral properties, and comparing results with classical string theory.

Contribution

It introduces a general framework for Drinfel'd twisted spin chains, constructs explicit maps to undeformed models, and initiates spectral analysis for non-abelian twisted integrable systems.

Findings

Identified a unique supergravity deformation with constant dilaton.

Developed a twisted-boundary approach to spectral problems.

Found the ground state deformation matches classical string results.

Abstract

We study the proposed integrable spin chain formulation of Jordanian deformations of the $AdS_5\times S^5$ superstring, realised via Drinfel'd twists. Among these models, we first identify a unique supergravity deformation confined to an $SL(2,\mathbb{R})$ sector and with constant dilaton. We then develop a general framework for closed Drinfel'd twisted spin chains and construct an explicit map to undeformed models with twisted-boundary conditions. Applied to the non-compact $\mathrm{XXX}_{-1/2}$ spin chain, the Jordanian twist breaks the Cartan generator labelling magnon excitations, obstructing the standard Bethe methods. Instead, using the twisted-boundary formulation, we initiate the spectral problem based on a residual root generator both in the continuum limit and for short chains. We find that the ground state is non-trivially deformed, and is in agreement with the classical string result, while our analysis does not capture higher-spin excited states. We also study the asymptotics of the associated $Q$-system, which is well-behaved and compatible with the boundary-twist. While a full understanding of the spectrum remains open, our work provides concrete steps toward a spectral description of non-abelian twisted integrable models.