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

在2000-2002年的研究期间，获得了以下结果：1。SU(2)_L × U(1)_Y电弱规范理论中规范异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。由此，我们证明了如果超荷Σ_γY_γ= 0和Σ_γY ^3_γ = 0的无异常条件满足，晶格SU(2)_L × U(1)_Y电弱规范理论中的规范异常在有限晶格间距上完全抵消。利用畴壁费米子构造手性规范理论的规范不变性我们直接利用畴壁费米子构造了具有精确规范不变性的手性规范理论。由畴壁费米子产生的陈氏-西蒙斯电流可以用来构造一个5 + 1维拓扑场，对拓扑场进行上同调分析可以得到一个规范不变的5维计数器项。这一结果在第19届晶格场理论国际研讨会（lattice 2001, August 19-24, Berlin）上作为全体会议报告。具有精确规范不变性的阿贝尔手性规范理论的实际构造迄今为止，仅在无异常的阿贝尔手性规范理论中获得了Weyl费米子测度的完备的规范不变性构造（Luscher 1999）。通过考虑可容许U(1)规范域原空间的Z_N子空间，给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种应用。

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.