Integrable models: from dynamical solutions to string theory

TL;DR

This paper reviews integrable models, their dynamical properties, and their applications in string theory, highlighting the Bethe Ansatz solution for an SO(6) symmetric Hamiltonian with boundary conditions.

Contribution

It provides a comprehensive overview of integrable models, including detailed discussions and new insights into their role in string theory and boundary solutions.

Findings

Analysis of integrability conditions and dynamics

Detailed discussion of specific integrable models

Bethe Ansatz solution for SO(6) Hamiltonian with boundary

Abstract

We review the status of integrable models from the point of view of their dynamics and integrability conditions. Some integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the Bethe Ansatz solution of the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the seventieth anniversaries of Andr\'{e} Swieca (in memoriam) and Roland K\"{o}berle.