Fermions and Kaluza-Klein vacuum decay: a toy model

TL;DR

This paper investigates whether twisted fermions can prevent the decay of the Kaluza-Klein vacuum by analyzing a simplified (1+1)-dimensional model, finding that they do not provide stabilization.

Contribution

It introduces a toy model to study fermion effects on vacuum decay and calculates the fermion determinant, showing twisted fermions do not stabilize the vacuum.

Findings

Fermion determinant is finite in the toy model.

Twisted fermions do not suppress Kaluza-Klein vacuum decay.

Abstract

We address the question of whether or not fermions with twisted periodicity condition suppress the semiclassical decay of M^4xS^1 Kaluza--Klein vacuum. We consider a toy (1+1)-dimensional model with twisted fermions in cigar-shaped Euclidean background geometry and calculate the fermion determinant. We find that contrary to expectations, the determinant is finite. We consider this as an indication that twisted fermions do not stabilize the Kaluza--Klein vacuum.