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Worldline Approach to Chiral Fermions on the Lattice

Presenter: Kurt Langfeld — University of Plymouth

Kurt Langfeld, Gerald Dunne, Holger Gies, Klaus Klingmuller

We propose to apply "worldline numerics" to a numerical calculation of quark determinants. The 1+1 dimensional 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 the chiral symmetry exactly. Numerical results for selected scalar condensate background fields are shown and compared with analytical results where available. The case of finite temperature and finite fermion chemical potential is also briefly discussed.