A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices

TL;DR

This paper constructs and analyzes open-chain transfer matrices using q-deformed su(2|2) S-matrices, highlighting the importance of a key factor for their commutativity, which is essential for integrability.

Contribution

It extends Sklyanin's construction to the q-deformed su(2|2) case, including graded versions, and emphasizes the role of a crucial factor for transfer matrix commutativity.

Findings

Constructed commuting open-chain transfer matrices from q-deformed su(2|2) S-matrices.

Identified a crucial factor ensuring the commutativity of transfer matrices.

Highlighted the role of crossing symmetry in the construction.

Abstract

In this note, we perform Sklyanin's construction of commuting open-chain/boundary transfer matrices to the q-deformed SU(2|2) bulk S-matrix of Beisert and Koroteev and a corresponding boundary S-matrix. This also includes a corresponding commuting transfer matrix using the graded version of the q-deformed bulk S-matrix. Utilizing the crossing property for the bulk S-matrix, we argue that the transfer matrix for both graded and non-graded versions contains a crucial factor which is essential for commutativity.