# Introduction to the nested algebraic Bethe ansatz

### 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:
Editor-in-charge assigned

We changed the text according to the referee's comments.

### 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

Resubmission 1911.12811v2 on 31 July 2020
Submission 1911.12811v1 on 22 April 2020

## Reports on this Submission

### Strengths

Excellent lecture notes on the Nested Algebraic Bethe Ansatz.

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.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Strengths

As in my previous report

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

• validity: high
• significance: high
• originality: top
• clarity: high
• formatting: excellent
• grammar: good