Revisiting the Y=0 open spin chain at one loop

TL;DR

This paper proves the integrability of a specific open spin chain Hamiltonian related to Y=0 giant gravitons by constructing its transfer matrix, deriving eigenvalues and Bethe equations, and comparing with all-loop proposals.

Contribution

It constructs the transfer matrix for the Y=0 open spin chain, directly proving its integrability and analyzing its Bethe ansatz solutions.

Findings

Transfer matrix constructed and eigenvalues derived.

Bethe equations obtained and compared with all-loop proposals.

Identified gauge freedom in Bethe ansatz solutions.

Abstract

In 2005, Berenstein and Vazquez determined an open spin chain Hamiltonian describing the one-loop anomalous dimensions of determinant-like operators corresponding to open strings attached to Y=0 maximal giant gravitons. We construct the transfer matrix (generating functional of conserved quantities) containing this Hamiltonian, thereby directly proving its integrability. We find the eigenvalues of this transfer matrix and the corresponding Bethe equations, which we compare with proposed all-loop Bethe equations. We note that the Bethe ansatz solution has a certain "gauge" freedom, and is not completely unique.