Some Constant Solutions to Zamolodchikov's Tetrahedron Equations

TL;DR

This paper presents specific constant solutions to Zamolodchikov's tetrahedron equations, expanding the known solution space through direct solving methods and new ansatz approaches.

Contribution

It introduces new two-dimensional constant solutions to the tetrahedron equations using direct solving techniques and novel ansatz methods.

Findings

New constant solutions to tetrahedron equations identified

Solutions derived from upper triangular and Zamolodchikov's ansatz

Expands understanding of solution construction methods

Abstract

In this letter we present constant solutions to the tetrahedron equations proposed by Zamolodchikov. In general, from a given solution of the Yang-Baxter equation there are two ways to construct solutions to the tetrahedron equation. There are also other kinds of solutions. We present some two-dimensional solutions that were obtained by directly solving the equations using either an upper triangular or Zamolodchikov's ansatz.