Sequential Bethe vectors and the quantum Ernst system

TL;DR

This paper reviews how Bethe ansatz techniques are used to construct solutions for the quantum Ernst system, focusing on limits that connect different Bethe systems and explore semiclassical behavior.

Contribution

It introduces the concept of sequential Bethe vectors and analyzes the semiclassical limit within the Bethe ansatz framework for the quantum Ernst system.

Findings

Linking Bethe systems with different insertions via critical limits

Introduction of sequential Bethe vectors

Analysis of semiclassical limit of the system

Abstract

We give a brief review on the use of Bethe ansatz techniques to construct solutions of recursive functional equations which emerged in a bootstrap approach to the quantum Ernst system. The construction involves two particular limits of a rational Bethe ansatz system with complex inhomogeneities. First, we pinch two insertions to the critical value. This links Bethe systems with different number of insertions and leads to the concept of sequential Bethe vectors. Second, we study the semiclassical limit of the system in which the scale parameter of the insertions tends to infinity.