Study of the complex fermion determinant in a $\rm U(1)_L \otimes U(1)_R$ symmetric Yukawa model

TL;DR

This paper investigates the phase fluctuations of the fermion determinant in a U(1) symmetric Yukawa model with mirror fermions, finding minimal phase fluctuations that suggest feasible numerical simulations.

Contribution

It provides an analysis of the complex phase behavior of the fermion determinant in a specific chiral lattice model, demonstrating small phase fluctuations for relevant parameters.

Findings

Complex phase fluctuations are very small, around 2 x 10^{-3}.

The results suggest potential for numerical simulation of the model.

The study focuses on a physically relevant parameter regime.

Abstract

Lattice theories that contain chiral multiplets of fermions can have complex fermion determinants. This is for example the case for the $\rm U(1)_L \otimes U(1)_R$ symmetric Yukawa model with mirror fermions, if the number of generations of fermions and mirror fermions is odd. Whether a numerical simulation of such a model is possible depends on the magnitude of fluctuations of the complex phase factor of the fermion determinant. We investigate the fermion determinant of the U(1) Yukawa model with mirror fermions for a physically relevant choice of parameters. The argument of the complex phase turns out to fluctuate only very little and is at most of the order of $2 \cdot 10^{-3}$.