Revisiting the Y = 0 open spin chain at one loop

In 2005, Berenstein and Vázquez 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.