Worldline Approach to Chiral Fermions

TL;DR

This paper introduces a worldline numerics method for calculating quark determinants, demonstrating its effectiveness and chiral symmetry preservation through tests on the Gross-Neveu model with finite chemical potential.

Contribution

It presents a novel application of worldline numerics to compute quark determinants with exact chiral symmetry preservation and analytic renormalisation.

Findings

Numerical results agree with analytical solutions for kink configurations.

The method preserves chiral symmetry exactly during discretisation.

Finite chemical potential cases are briefly discussed.

Abstract

We propose to apply ``worldline numerics'' to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of the worldlines, which is central to the numerical treatment, preserves chiral symmetry exactly. Numerical results for a kink configuration as a scalar background field are shown and compared with analytical results. The case of finite fermion chemical potential is also briefly discussed.