Yangian-invariant field theory of matrix-vector models

TL;DR

This paper develops a Yangian-invariant field theory for matrix-vector models, describing one-dimensional spin particles with a Hamiltonian that incorporates collective bosonic and current algebra interactions, enabling spectrum calculations.

Contribution

It constructs a new Yangian-su(R) invariant Hamiltonian for matrix-vector models, including cubic-current terms for R ≥ 3, and demonstrates explicit spectrum computation in simple cases.

Findings

Hamiltonian exhibits Yangian symmetry with cubic-current interactions for R ≥ 3

Spectrum can be explicitly computed in simplified subspaces

Provides a field-theoretic framework for matrix-vector models with spin

Abstract

We extend our study of the field-theoretic description of matrix-vector models and the associated many-body problems of one dimensional particles with spin. We construct their Yangian-su(R) invariant Hamiltonian. It describes an interacting theory of a c=1 collective boson and a k=1 su(R) current algebra. When $R \geq 3$ cubic-current terms arise. Their coupling is determined by the requirement of the Yangian symmetry. The Hamiltonian can be consistently reduced to finite-dimensional subspaces of states, enabling an explicit computation of the spectrum which we illustrate in the simplest case.