Fractionally charged extended objects and superselection rules

TL;DR

This paper explores how topological objects with zero-energy fermion modes can acquire fractional charges, leading to superselection rules that prevent their decay, with implications for cosmology and condensed matter physics.

Contribution

It introduces a superselection rule for fractionally charged topological objects with zero-energy fermion modes, extending understanding of their stability.

Findings

Objects with half-integer fermion number cannot decay in isolation.

Zero-energy modes can be assigned negative fermion numbers, forming a 'Majorana pond'.

Superselection rules prevent decay of metastable configurations with fractional charge.

Abstract

Topological objects resulting from symmetry breakdown may be either stable or metastable depending on the pattern of symmetry breaking. However, if they trap zero-energy modes of fermions, and in the process acquire non-integer fermionic charge, the metastable configurations also get stabilized. In the case of Dirac fermions the spectrum of the number operator shifts by 1/2. In the case of majorana fermions it becomes useful to assign negative values of fermion number to a finite number of states occupying the zero-energy level, constituting a \textit{majorana pond}. We determine the parities of these states and prove a superselection rule. Thus decay of objects with half-integer fermion number is not possible in isolation or by scattering with ordinary particles. The result has important bearing on cosmology as well as condensed matter physics.