Jordanian spin chains for twisted strings in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>AdS</mml:mi> <mml:mn>5</mml:mn> </mml:msub> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>5</mml:mn>

We study the proposed integrable spin chain formulation of Jordanian deformations of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>AdS</a:mi> <a:mn>5</a:mn> </a:msub> <a:mo>×</a:mo> <a:msup> <a:mi>S</a:mi> <a:mn>5</a:mn> </a:msup> </a:math> superstring, realized via Drinfel’d twists. Among these models, we first identify a unique supergravity deformation confined to an <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>S</c:mi> <c:mi>L</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>2</c:mn> <c:mo>,</c:mo> <c:mi mathvariant="double-struck">R</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> 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 noncompact <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>XXX</h:mi> <h:mrow> <h:mo>−</h:mo> <h:mn>1</h:mn> <h:mo>/</h:mo> <h:mn>2</h:mn> </h:mrow> </h:msub> </h:math> spin chain, the Jordanian twist breaks the Cartan generator labeling 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 nontrivially 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 <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>Q</j:mi> </j:math> 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.