Regularising spectral curves for homogeneous Yang-Baxter strings

In this Letter, we study the semi-classical spectrum of integrable worldsheet -models using the Spectral Curve.We consider a Homogeneous Yang-Baxter deformation of the 5 × 5 superstring, understood as the composition of a Jordanian with a "non-diagonal" TsT deformation.We derive its type IIB supergravity solution, whose isometry algebra features zero supercharges and a non-relativistic conformal algebra in 0 + 1 dimensions.While the Spectral Curves of non-diagonal TsT models are ill-defined, we demonstrate that the composition with a Jordanian model regularises this issue.From the regularised Curve, we derive the one-loop shift of the classical energy and the semi-classical spectrum of excitations of a point-like string.In the TsT limit, the one-loop shift vanishes despite the loss of supersymmetry.Our results suggest that it may be possible to use standard Bethe Ansatze on spin chain pictures of deformed  = 4 Super-Yang-Mills theory dual to non-diagonal TsT models.One of the earliest and most robust validations of the AdS/CFT correspondence is the match between the energy spectrum of the 5 × 5 -model and the scaling dimensions for various operators of planar  = 4 Super-Yang-Mills (SYM) theory.Crucial for this achievement was the use of an underlying integrable model and the development of new integrability techniques to solve for the exact spectrum in certain sectors.Particularly well-understood is the spectrum of long operators dual to semi-classical string configurations which are amenable to the algebraic Bethe Ansatz and the semi-Classical Spectral Curve (s-CSC) respectively, as reviewed in [1].The success of AdS/CFT integrability has spurred, among other factors, significant interest in integrable deformations of string -models,