Fermions with a bounded and discrete mass spectrum

TL;DR

This paper introduces a mechanism to generate a finite, discrete spectrum of fermion masses in four dimensions using a scalar domain wall in five dimensions, with potential applications in condensed matter physics.

Contribution

It presents an analytical method to obtain a bounded, discrete fermion mass spectrum via a specific Yukawa coupling and scalar potential in a higher-dimensional setup.

Findings

Analytical derivation of a discrete fermion mass spectrum

Mass values depend on Yukawa coupling and scalar potential parameters

Potential application to condensed matter fermions in lower dimensions

Abstract

A mechanism for determining fermion masses in four spacetime dimensions is presented, which uses a scalar-field domain wall extending in a fifth spacelike dimension and a special choice of Yukawa coupling constants. A bounded and discrete fermion mass spectrum is obtained analytically for spinors localized in the fifth dimension. These particular mass values depend on a combination of the absolute value of the Yukawa coupling constant and the parameters of the scalar potential. A similar mechanism for a finite mass spectrum may apply to $(1+1)$--dimensional fermions relevant to condensed matter physics.