The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix

TL;DR

This paper explores the mathematical structure of the AdS5 x S5 string theory S-matrix, revealing its relation to the Hubbard model's R-matrix and clarifying the underlying algebraic framework from an AdS/CFT perspective.

Contribution

It introduces a new understanding of the Tetrahedron Zamolodchikov algebra's role in the AdS5 x S5 S-matrix, connecting it to the Hubbard model's R-matrix and providing a clearer algebraic interpretation.

Findings

The S-matrix decomposes into two su(2|2) components related to the Hubbard model.

The Hubbard model's R-matrix can be interpreted through the Tetrahedron Zamolodchikov algebra.

Clarification of the algebraic structure underlying the AdS/CFT integrability framework.

Abstract

The S-matrix of the $AdS_5 \times S^5$ string theory is a tensor product of two centrally extended su(2|2) S-matrices, each of which is related to the R-matrix of the Hubbard model. The R-matrix of the Hubbard model was first found by Shastry, who ingeniously exploited the fact that, for zero coupling, the Hubbard model can be decomposed into two XX models. In this article, we review and clarify this construction from the AdS/CFT perspective and investigate the implications this has for the $AdS_5 \times S^5$ S-matrix.