Some eigenstates for a model associated with solutions of tetrahedron equation

TL;DR

This paper constructs specific eigenstates for a 2+1-dimensional integrable model linked to the tetrahedron equation, including particle-like and string-like states, extending Bethe ansatz concepts to higher dimensions.

Contribution

It introduces explicit eigenstates for a 2+1D model related to the tetrahedron equation, including novel particle-like and string-like solutions.

Findings

Eigenstates include one-particle, two-particle, and string-like states.

Construction is analogous to Bethe ansatz methods in 1+1 dimensions.

Provides explicit solutions for a higher-dimensional integrable model.

Abstract

Here we present some eigenstates for a 2+1-dimensional model associated with a solution of the tetrahedron equation. The eigenstates include those "particle-like" (namely one-particle and two-particle ones), constructed in analogy with the usual 1+1-dimensional Bethe ansatz, and some simple "string-like" ones.