# Introduction to the nested algebraic Bethe ansatz

### Submission summary

 Authors (as Contributors): Nikita Slavnov
Submission information
Date accepted: 2020-08-26
Date submitted: 2020-07-31 18:29
Submitted by: Slavnov, Nikita
Submitted to: SciPost Physics Lecture Notes
Ontological classification
Specialties:
• 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.

Published as SciPost Phys. Lect. Notes 19 (2020)

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

### Report

For the revised version the author has carefully edited his manuscript following the suggestions of the four referees. This further improved the quality. In particular, he has added more explanatory text at the beginning of each section which makes the lecture notes more accessible to learners.

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

### 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