# Separation of Variables for a flux tube with an end

## TL;DR

This paper uncovers an integrable structure in a specific limit of a correlation function involving the stress-tensor multiplet, modeled as an open spin chain with a dynamical boundary, solved via Baxter and Separation of Variables techniques.

## Contribution

It introduces a novel integrable model of a flux tube with a dynamical boundary and provides its solution using advanced integrability methods.

## Key findings

- Identification of an integrable open spin chain with a dynamical boundary
- Solution of the model using Baxter operator and Separation of Variables
- Eigenvalues encode excitations' rapidities and dynamics

## Abstract

We consider a partial light-cone limit of a correlation function of the stress-tensor multiplet and identify an integrable structure emerging at one loop order of perturbation theory. It corresponds to a noncompact open spin chain with one boundary being recoil-less while the other one fully dynamical. We solve the system by means of techniques of the Baxter operator and Separation of Variables. The eigenvalues of separated variables define rapidities of excitations propagating on the color flux tube and encode their factorizable dynamics in the presence of a dynamical boundary.