Ginsparg-Wilson Fermions in Odd Dimensions

Details Ginsparg-Wilson Fermions in Odd Dimensions Ginsparg-Wilson Fermions in Odd Dimensions

2000-12-17

arxiv.org/abs/hep-lat/0012020v2

JHEP 0107:015,2001

Physics

High Energy Physics

High Energy Physics - Lattice

15 pages, no figures, final version published in JHEP

Scientific paper

10.1088/1126-6708/2001/07/015

The Ginsparg-Wilson relation, if written in a suitable form, can be used as a condition for lattice Dirac operators of massless fermions also in odd dimensions. The fermion action with such a Dirac operator is invariant under a generalized parity transformation, which reduces to the ordinary parity transformation in the (naive) continuum limit. The fermion measure, however, transforms non-trivially under the generalized parity transformation, and hence the parity anomaly arises solely from the fermion measure. The analogy to the lattice construction of chiral gauge theories in even dimensions is clarified by considering a dimensional reduction. We also propose a natural definition of a lattice Chern-Simons term, which is consistent with odd dimensional Ginsparg-Wilson fermions.

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