标题： 格点上的超对称性和乘积法则 显示英文标题

标题： Supersymmetry on the lattice and the Leibniz rule

摘要： 对格点上超对称理论的主要障碍是乘积法则的失效。 我们通过使用Wess-Zumino模型和一个一般的Ginsparg-Wilson算子来分析这个问题，该算子是局部的且没有物种倍增问题。 我们指出，如果任何场变量所携带的一般动量$k_{\mu}$在极限$a\to 0$下满足$|ak_{\mu}|<\delta$，对于任意小但有限的$\delta$而言，乘积法则可以在格点上保持。 如果理论在微扰下是有限的，并且离散化不会引起进一步的对称性破缺，则预计这一条件通常会得到满足。 因此，我们首先通过应用保持超对称性的高阶导数正则化方法，使连续的Wess-Zumino模型有限。 然后我们将该理论放在格点上，除了由于乘积法则失效导致相互作用项中的对称性破缺外，该理论保持了超对称性。 通过这种方式，我们定义了一个保持基本性质如$U(1)\times U(1)_{R}$对称性和全纯性的格点Wess-Zumino模型。 我们证明，该模型在极限$a\to 0$下可以再现连续理论，直到微扰理论中的任意有限阶；从这个意义上说，由乘积法则失效引起的所有的超对称性破缺项都是无关的。 随后，我们建议这种离散化方法可能以非微扰的方式定义低能有效理论。 显示英文摘要

摘要： The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. We point out that the Leibniz rule could be maintained on the lattice if the generic momentum $k_{\mu}$ carried by any field variable satisfies $|ak_{\mu}|<\delta$ in the limit $a\to 0$ for arbitrarily small but finite $\delta$. This condition is expected to be satisfied generally if the theory is finite perturbatively, provided that discretization does not induce further symmetry breaking. We thus first render the continuum Wess-Zumino model finite by applying the higher derivative regularization which preserves supersymmetry. We then put this theory on the lattice, which preserves supersymmetry except for a breaking in interaction terms by the failure of the Leibniz rule. By this way, we define a lattice Wess-Zumino model which maintains the basic properties such as $U(1)\times U(1)_{R}$ symmetry and holomorphicity. We show that this model reproduces continuum theory in the limit $a\to 0$ up to any finite order in perturbation theory; in this sense all the supersymmetry breaking terms induced by the failure of the Leibniz rule are irrelevant. We then suggest that this discretization may work to define a low energy effective theory in a non-perturbative way.