Nonperturbative comstruction of the standard model based on the Ginsparg-Wilson relation

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During the research period of 2000-2002, the following results were obtained :1. Exact cancellation of gauge anomalies in SU(2)_L × U(1)_Y electroweak gauge theoryWe performed a cohomological analysis of of the 4 + 2-dimensional topological field introduced by Luscher (1999). Through this, we have shown that if the anomaly-free conditions in terms of the hypercharge, Σ_γY_γ= 0 and Σ_γ Y^3_γ = 0, are satisfied, the gauge anomalies in lattice SU(2)_L × U(1)_Y electroweak gauge theory cancel exactly at a finite lattice spacing.2. A gauge-invariant construction of chiral gauge theories using domain wall fermionWe constructed chiral gauge theories with exact gauge invariance directly using domain wall fermion. The chern-simons current induced from the domain wall fermion can be used to construct a 5 + 1-dimensional topological field, and the cohomological analysis of the topological field leads to a gauge-invariant 5-dimensional counter term.This result was reported in the XIX international symposium on lattice field theory (Lattice 2001, August 19-24, Berlin) as a plenary talk.3. A practical construction of abelian chiral gauge theories with exact gauge invarianceSo far, a complete gauge-invariant construction of the measure of Weyl fermions is obtained only for anomaly-free abelian chiral gauge theories (Luscher 1999). We proposed a practical implementation of this construction by considering the Z_N subspace of the original space of the admissible U(1) gauge fields.4. Applications of the Ginsparg-Wilson relationWe examined several applications of the Ginsparg-Wilson fermions to supersymmetric lattice models and matrix models.