格点Wess-Zumino模型与Ginsparg-Wilson费米子：单圈结果和GPU基准
Lattice Wess-Zumino model with Ginsparg-Wilson fermions: One-loop results and GPU benchmarks
摘要：
我们用数值方法计算了用重叠（Neuberger）簇的Ginsparg-Wilson费米子以及辅助费米子（加上超伴子）在晶格上建立的四维Wess-Zumino模型的单圈反项，使得晶格版本的$U(1)_R$对称性在裸质量消失的极限下完全保持。我们证实了其他作者以前的发现，在一个循环中没有重整化的超势的晶格理论，但有一个不匹配的波函数重整化的辅助字段。我们研究的狄拉克算子的范围，结果时，辅助费米子被整合出来，并显示本地化确实发生，但它是不太明显的指数本地化的重叠算子。我们还提出了这个模型的初步模拟结果，并概述了非微扰改进的晶格超导通过测量超对称沃德恒等式的战略。与此相关，我们的图形处理单元代码提供了一些基准。我们的模拟结果发现一个几乎为零的真空期望值的辅助领域，在弱耦合近似超对称性一致。
英文摘要：
We numerically evaluate the one-loop counterterms for the four-dimensional Wess-Zumino model formulated on the lattice using Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of $U(1)_R$ symmetry is exactly preserved in the limit of vanishing bare mass. We confirm previous findings by other authors that at one loop there is no renormalization of the superpotential in the lattice theory, but that there is a mismatch in the wavefunction renormalization of the auxiliary field. We study the range of the Dirac operator that results when the auxiliary fermion is integrated out, and show that localization does occur, but that it is less pronounced than the exponential localization of the overlap operator. We also present preliminary simulation results for this model, and outline a strategy for nonperturbative improvement of the lattice supercurrent through measurements of supersymmetry Ward identities. Related to this, some benchmarks for our graphics processing unit code are provided. Our simulation results find a nearly vanishing vacuum expectation value for the auxiliary field, consistent with approximate supersymmetry at weak coupling.
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