Article

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

09/2003; DOI:doi:10.1088/1126-6708/2004/12/006
Source: arXiv

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 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. Comment: revised version, 35pages, using JHEP3.cls

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### Keywords

abelian chiral gauge theories

cohomologically trivial part

finite lattice

gauge anomaly

gauge-invariant construction

Ginsparg-Wilson relation

JHEP3.cls

lattice

local cohomology problem

local counter term

Poincar\'e lemma

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