Regularising Spectral Curves for Homogeneous Yang-Baxter strings

TL;DR

This paper analyzes the semi-classical spectrum of integrable worldsheet sigma-models with a focus on a specific deformation of the $AdS_5\times S^5$ superstring, demonstrating how spectral curve regularization enables spectrum computation.

Contribution

It introduces a regularization method for spectral curves in non-diagonal TsT models, allowing for the calculation of quantum corrections in deformed superstring theories.

Findings

Regularized spectral curves enable spectrum analysis.

One-loop energy shift vanishes in TsT limit.

Potential for applying Bethe Ansatz to deformed theories.

Abstract

In this Letter, we study the semi-classical spectrum of integrable worldsheet $\sigma$-models using the Spectral Curve. We consider a Homogeneous Yang-Baxter deformation of the $AdS_5\times S^5$ 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 $N=4$ Super-Yang-Mills theory dual to non-diagonal TsT models.