# Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry

## TL;DR

This paper derives a general formula for the norm of eigenstates in quantum integrable models with $rak{gl}(m|n)$ symmetry, confirming a generalized Gaudin hypothesis.

## Contribution

It introduces a method to compute the norm of Bethe eigenstates in models with $rak{gl}(m|n)$ symmetry, establishing their properties and confirming the generalized Gaudin hypothesis.

## Key findings

- Norm of eigenstates is computed explicitly.
- Norm satisfies specific properties that determine it uniquely.
- Jacobian of Bethe equations shares the same properties.

## Abstract

We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(m|n)$-invariant $R$-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system of Bethe equations obeys the same properties. In this way we prove a generalized Gaudin hypothesis for the norm of the Hamiltonian eigenstates.