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We consider the model in two dimensions with boundary quadratic deformation(BQD), which has been discussed in tachyon condensation. The partition functionof this model (BQD) on a cylinder is determined, using the method of zetafunction regularization. We show that, for closed channel partition function, asubtraction procedure must be introduced in order to reproduce the correctresults at conformal points. The boundary entropy (g-function) is determinedfrom the partition function and the off-shell boundary state. We propose andconsider a supersymmetric generalization of BQD model, which includes aboundary fermion mass term, and check the validity of the subtractionprocedure.Comment: 21 pages, LaTeX, comments and 3 new references adde

Normalization of off-shell boundary state,g-function and zeta function regularization