We analyze zero energy solutions of the Dirac equation in the background of a stringlike configuration in an extension of the standard model that accommodates the most general fermionic mass matrix for neutrinos. If either the left- or the right-handed Majorana mass vanishes, neutrino and electron zero modes are found to exist. If the harmonic mean of the neutrino Majorana masses is large compared to the Dirac mass, we can prove that normalizable neutrino zero modes cease to exist. This leads to an odd number of fermionic zero modes - namely, only the electron zero mode - which we argue implies that the bosonic background is in a topologically distinct sector from the vacuum. This is confirmed by noting that the bosonic sector of the model involves the breaking of a global U(1) symmetry and hence possesses topological global U(1) strings.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)