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

在2000-2002年的研究期间，取得了以下成果：1. SU（2）_L × U（1）_Y电弱规范理论中规范反常的精确消去我们对Luscher（1999）提出的4 + 2维拓扑场进行了上同调分析。通过这一过程，我们证明了在满足超荷无反常条件时，SU（2）_L × U（1）_Y电弱规范理论中的规范反常在有限格距处完全抵消.用畴壁费米子构造规范不变性的手征规范理论我们直接用畴壁费米子构造了具有精确规范不变性的手征规范理论。利用畴壁费米子诱导的Chern-Simons电流可以构造一个5 + 1维拓扑场，通过对拓扑场的上同调分析，得到一个规范不变的5维反项.这一结果已在第十九届格点场论国际研讨会（Lattice 2001，August 19-24，柏林）上作为全体会议报告.具有精确规范不变性的阿贝尔手征规范理论的一个实际构造到目前为止，只对无反常的阿贝尔手征规范理论给出了Weyl费米子测度的一个完整的规范不变性构造（Luscher 1999）。通过考虑U（1）规范场原空间的Z_N子空间，我们提出了这种构造的一个实际实现. Ginsparg-Wilson关系的应用我们研究了Ginsparg-Wilson费米子在超对称晶格模型和矩阵模型中的几个应用。

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.