Can an odd number of fermions be created due to chiral anomaly?

TL;DR

This paper explores the theoretical possibility of creating an odd number of fractionally charged fermions in a 1+1 dimensional Abelian Higgs model, highlighting its consistency with symmetries and implications for higher dimensions.

Contribution

It demonstrates that odd fermion number creation is possible in 1+1D models without symmetry violation and constructs a proper fermionic determinant relevant for realistic models.

Findings

Odd number of fermions can be created without symmetry violation.

Proper fermionic determinant definition reveals non-trivial features.

Implications for fermion number violation in higher dimensions.

Abstract

We describe a possibility of creation of an odd number of fractionally charged fermions in 1+1 dimensional Abelian Higgs model. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor makes it mathematically inconsistent. We construct the proper definition of the fermionic determinant in this model and underline its non-trivial features that are of importance for realistic 3+1 dimensional models with fermion number violation.