Can baryogenesis occur on the lattice?

TL;DR

This paper investigates whether baryogenesis can occur in lattice models of the Standard Model with conserved fermion number, demonstrating fermion creation via spectral flow despite conservation laws.

Contribution

It provides an explicit computation of spectral flow in lattice models, showing how fermion creation can happen even with exact fermion number conservation.

Findings

Fermion creation occurs through spectral flow in lattice models.

Spectral flow enables baryogenesis mechanisms despite conserved fermion number.

Comparison with the Schwinger model illustrates similar particle creation mechanisms.

Abstract

We examine the question of how baryogenesis can occur in lattice models of the Standard Model where there is a global $U(1)$ symmetry which is accompanied by an exactly conserved fermion number. We demonstrate that fermion creation and annihilation can occur in these models {\em despite} this exact fermion number conservation, by explicitly computing the spectral flow of the hamiltonian in the two dimensional U(1) axial model with Wilson fermions. For comparison we also study the closely related Schwinger model where a similar mechanism gives rise to anomalous particle creation and annihilation.