A Note on Fermion and Gauge Couplings in Field Theory Models for Tachyon Condensation

TL;DR

This paper investigates soliton solutions in supersymmetric scalar field theories, analyzing fermionic and bosonic zero-modes, gauge couplings, and the spectrum of fluctuation modes, revealing that only the zero mode is normalizable.

Contribution

It compares different gauge couplings in supersymmetric models and shows that only the zero mode is normalizable, with the fluctuation spectrum being identical across scalar, fermion, and gauge fields.

Findings

Born-Infeld coupling yields one normalizable zero mode

Other gauge couplings have no normalizable modes

Spectrum of fluctuations is identical for scalar, fermion, and gauge fields

Abstract

We study soliton solutions in supersymmetric scalar field theory with a class of potentials. We study both bosonic and fermionic zero-modes around the soliton solution. We study two possible couplings of gauge fields to these models. While the Born-Infeld like coupling has one normalizable mode (the zero mode), the other kind of coupling has no normalizable modes. We show that quantum mechanical problem which determines the spectrum of fluctuation modes of the scalar, fermion and the gauge field is identical. We also show that only the lowest lying mode, i.e., the zero mode, is normalizable and the rest of the spectrum is continuous.