Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

Details Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

2003-09-07

arxiv.org/abs/hep-lat/0309022v2

JHEP 0412:006,2004

Physics

High Energy Physics

High Energy Physics - Lattice

revised version, 35pages, using JHEP3.cls

Scientific paper

10.1088/1126-6708/2004/12/006

In the gauge-invariant construction of abelian chiral gauge theories on the lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topological and its cohomologically trivial part plays the role of the local counter term. We give a prescription to solve the local cohomology problem within a finite lattice by reformulating the Poincar\'e lemma so that it holds true on the finite lattice up to exponentially small corrections. We then argue that the path-integral measure of Weyl fermions can be constructed directly from the quantities defined on the finite lattice.

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