Normalization of Off-shell Boundary State, g-function and Zeta Function Regularization

TL;DR

This paper analyzes a two-dimensional boundary quadratic deformation model using zeta function regularization, focusing on the boundary entropy and off-shell boundary states, and extends it to a supersymmetric case.

Contribution

It introduces a subtraction procedure for the partition function to correctly reproduce conformal results and proposes a supersymmetric generalization of the model.

Findings

Partition function determined via zeta function regularization.

Subtraction procedure needed for correct conformal limit results.

Supersymmetric extension includes boundary fermion mass term.

Abstract

We consider the model in two dimensions with boundary quadratic deformation (BQD), which has been discussed in tachyon condensation. The partition function of this model (BQD) on a cylinder is determined, using the method of zeta function regularization. We show that, for closed channel partition function, a subtraction procedure must be introduced in order to reproduce the correct results at conformal points. The boundary entropy (g-function) is determined from the partition function and the off-shell boundary state. We propose and consider a supersymmetric generalization of BQD model, which includes a boundary fermion mass term, and check the validity of the subtraction procedure.