Regularising spectral curves for homogeneous Yang-Baxter strings

Abstract

In this Letter, we study the semi-classical spectrum of integrable worldsheet σ-models using the Spectral Curve. We consider a Homogeneous Yang-Baxter deformation of the AdS5×S5 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 N=4 Super-Yang-Mills theory dual to non-diagonal TsT models.