On odd number of fermion zero modes on solitons in quantum field theory and string/M theory

TL;DR

The paper discusses how an odd number of Majorana fermion zero modes on solitons indicates an inconsistency in higher-dimensional quantum field theories and string/M theories, supported by specific examples.

Contribution

It establishes a criterion linking the parity of fermion zero modes on solitons to the consistency of theories in higher dimensions, with validation through examples.

Findings

Odd number of fermion zero modes signals inconsistency in higher-dimensional theories.

Validated the criterion in specific field theory and string/M theory examples.

Abstract

We argue that having an odd number of Majorana fermion zero modes on a dynamical point-like soliton signifies an inconsistency in a theory with 3+1 and higher dimensions. We check this statement in a couple of examples in field theory and in string/M theory.