## SciPost Submission Page

# Introduction to the nested algebraic Bethe ansatz

### by N. A. Slavnov

### Submission summary

As Contributors: | Nikita Slavnov |

Arxiv Link: | https://arxiv.org/abs/1911.12811v2 (pdf) |

Date submitted: | 2020-07-31 18:29 |

Submitted by: | Slavnov, Nikita |

Submitted to: | SciPost Physics Lecture Notes |

Discipline: | Physics |

Subject area: | Mathematical Physics |

Approach: | Theoretical |

### Abstract

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions and explicit formulas for the Bethe vectors. We also give a representation for the Bethe vectors in the form of a trace formula.

###### Current status:

### Author comments upon resubmission

### List of changes

We extend description of the application of the nested algebraic Bethe ansatz in physics.

We explain how off-shell Bethe vectors appear in calculations of matrix elements of local operators.

We give the explicit solution of the quantum inverse problem.

We mention a method to construct Bethe vectors via Sklyanin's B-operator.

The content of two appendices is moved to the main text.

The list of references is extended.

Typos are corrected

### Submission & Refereeing History

*You are currently on this page*

## Reports on this Submission

### Anonymous Report 1 on 2020-8-4 Invited Report

### Strengths

Excellent lecture notes on the Nested Algebraic Bethe Ansatz.

### Weaknesses

None

### Report

The manuscript was considerably improved by the author. The most essential suggestions from my previous report are taken into account. I specially appreciated the brief explanations in the beginning of each section. I think that these excellent lecture notes are perfectly suitable for publication in the Les Houches volume in its present form.

### Anonymous Report 2 on 2020-8-4 Invited Report

### Strengths

As in my previous report

### Weaknesses

No weaknesses

### Report

The author has implemented the remarks that I have suggested in my previous report. Thus, I suggest the publication of the manuscript in the current form.

### Requested changes

no changes