Numerical implementation of U(1) chiral lattice gauge theories in
two-dimensions
Presenter: Yoshio Kikukawa
Daisuke Kadoh, Yoshio Kikukawa
Abstract: We consider a numerical method to formulate U(1) chiral gauge theories on the lattice with exact gauge invariance. In two-dimensional case, the
gauge invariant Weyl fermion measure is explicitly worked out and the locality
and gauge-invarinace are checked. In our approach, the local cohomology problem is solved within a finite volume lattice by reformulating the Poincaré lemma
so that it holds true on the finite lattice up to exponentially small corrections.
With this solution, the fermion measure is reconstructed by the parameter integration performed with a Gaussian Quadrature formula, which turns out to
show rather good convergence for the admissible fields. We also examine the numerical implementation of the field tensor-based method for the cohomological
analysis, by which the parameter integration can be omitted completely.
(based on hep-lat/0309022, hep-lat/0401025, hep-lat/0504021)
1