A numerical solution to the local cohomology problem in U(1) chiral gauge theories

Details A numerical solution to the local cohomology problem in U(1) chiral gauge theories A numerical solution to the local cohomology problem in U(1) chiral gauge theories

2004-01-19

arxiv.org/abs/hep-lat/0401025v2

JHEP 0501:024,2005

Physics

High Energy Physics

High Energy Physics - Lattice

11pages, 6 figures, REVTeX4; references added

Scientific paper

10.1088/1126-6708/2005/01/024

We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincare lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties.

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