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We discussed subspaces of the N=1 supersymmetric sine-Gordon model withDirichlet boundaries through light-cone lattice regularization. In this paper,we showed, unlike the periodic boundary case, both of Neveu-Schwarz (NS) andRamond (R) sectors of a superconformal field theory were obtained. Using amethod of nonlinear integral equations for auxiliary functions defined byeigenvalues of transfer matrices, we found that an excitation state with an oddnumber of particles is allowed for a certain value of a boundary parameter evenon a system consisting of an even number of sites. In a small-volume limitwhere conformal invariance shows up in the theory, we derived conformaldimensions of states constructed through the lattice-regularized theory. Theresult shows existence of the R sector, which cannot be obtained from theperiodic system, while a winding number is restricted to an integer or ahalf-integer depending on boundary parameters.

Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach