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

D. Kadoh·Y. Kikukawa·Y. Nakayama
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Abstract

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 Poincaré 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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D. Kadoh, Y. Kikukawa, Y. Nakayama. 2005-01-14. Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice. https://doi.org/10.1088/1126-6708%2F2004%2F12%2F006

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