Boundary Effects on the Supersymmetric Sine-Gordon Model Through Light-Cone Lattice Regularization

Abstract

In this report, we discuss how the boundary condition of the spin-1 XXZ chain affects its low-energy effective field theory. The low-energy effective field theory of the spin-1 XXZ model is known as the supersymmetric (SUSY) sine-Gordon model. As a SUSY model, the theory consists of two subspaces called the Neveu–Schwarz (NS) sector and the Ramond (R) sector. In the Bethe-ansatz contest, the spin chain and its effective field theory are connected via the light-cone lattice regularization in the sense that these two models share the same transfer matrices. Conversely, the effective field theory is obtained in the scaling limit of the spin chain. Using the nonlinear integral equations (NLIEs) for the eigenvalues of the transfer matrices, we derived the scattering matrices of the SUSY sine-Gordon model from the large volume limit analysis of the spin-1 XXZ chain with boundary magnetic fields. At the same time, we derived the conformal dimensions of the SUSY sine-Gordon model in the small volume limit. From these quantities, we found that the different sector of the SUSY sine-Gordon model is realized from the spin-1 XXZ chain depending on the values of boundary magnetic fields.