Work

Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras

Year: 2024

Type: article

Abstract: Bethe Ansatz was discovered in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations [tetrahedron equation and d-simplex equations]. Here we describe a universal method to solve these equations using Clifford algebras. The Yang-Baxter equation (d=2), Zamolodchikov's tetrahedron equation (d=3) and the Bazhanov-Stroganov equation (d=4) are special cases. Our solutions form a linear space. This helps us to include spectral parameters. Potential applications are discussed.

Source: Nuclear Physics B

DOI: 10.1016/j.nuclphysb.2024.116664

Authors: Pramod Padmanabhan, Vladimir Korepin

Institutions: Indian Institute of Technology Bhubaneswar, Stony Brook University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: U.S. Department of Energy, Office of Science

Awards: G241279073, G357145406, G5765906131, G7463374569