晶格超对称性的一个判据：循环莱布尼兹规则
A criterion for lattice supersymmetry: cyclic Leibniz rule
摘要：
格点上违反莱布尼茨规则是构造格点超对称模型的一个障碍，这是一个古老的传说。虽然它仍然是真实的完全超对称，我们表明，稍微修改形式的莱布尼茨规则，我们称之为循环莱布尼茨规则（R1），实际上是一个标准的存在部分晶格超对称。在一维空间中，我们找到了在平移不变性和局部性等自然假设下，格上的格差算子和域乘法满足条件的集合。从而构造了一个不破坏定域性的超对称晶格量子力学模型。这种关系与格点Nicolai映射构造中所谓的表面项消失的条件是一致的。我们可以用任意的超势来构造超场体系。这也使我们能够安全地将局部化技术应用于我们的模型，因为我们的模型的动力学项和相互作用项在超对称变换下是独立不变的。在寻找解决方案的高维情况下的初步尝试也进行了讨论。
英文摘要：
It is old folklore that the violation of Leibniz rule on a lattice is an obstruction for constructing a lattice supersymmetric model. While it is still true for full supersymmetry, we show that a slightly modified form of the Leibniz rule, which we call cyclic Leibniz rule (CLR), is actually a criterion for the existence of partial lattice supersymmetry. In one dimension, we find sets of lattice difference operator and field multiplication smeared over lattice which satisfy the CLR under some natural assumptions such as translational invariance and locality. Thereby we construct a model of supersymmetric lattice quantum mechanics without spoiling locality. The CLR relation is coincident with the condition that the vanishing of the so-called surface term in the construction by lattice Nicolai map. We can construct superfield formalism with arbitrary superpotential. This also enables us to apply safely a localization technique to our model, because the kinetic term and the interaction terms of our model are independently invariant under the supersymmetry transformation. A preliminary attempt in finding a solution for the higher dimensional case is also discussed.
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