Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach
Abstract:
We discussed subspaces of the N=1 supersymmetric sine-Gordon model with Dirichlet boundaries through light-cone lattice regularization. In
this paper, we showed, unlike the periodic boundary case, both of Neveu-Schwarz (NS)
and Ramond (R) sectors of a superconformal field theory were obtained. Using a method of nonlinear integral equations for auxiliary functions
defined by eigenvalues of transfer matrices, we found that an excitation state with an odd number of particles is allowed for a certain value of a
boundary parameter even on a system consisting of an even number of sites. In a small-volume limit where conformal invariance shows up in the theory, we derived conformal dimensions of states constructed through the lattice-regularized theory. The result shows existence of the R sector,
which cannot be obtained from the periodic system, while a winding number is restricted to an integer or a half-integer depending on boundary parameters.
REFERENCE: arXiv:1404.3809