二维$\mathcal{N}=(2,2)$ SYM格点公式中的SUSY恒等式
SUSY WT identity in a lattice formulation of 2D $\mathcal{N}=(2,2)$ SYM
摘要：
本文讨论了二维$\mathcal{N}=(2,2)$ $SU(k)$超对称Yang-Mills理论（SYM）的Sugino格点公式中与超对称（SUSY）Ward-Takahashi（WT）恒等式有关的一些问题.一个微扰的论点表明，超对称WT恒等式在连续介质理论中再现连续极限，没有任何操作重整化/混合和调整的晶格参数。作为应用程序的晶格SUSY WT身份，我们表明，在这个晶格配方中的哈密顿密度的处方，提出了由Kanamori，杉野和铃木，也是合理的，从正确规范化的超电流之间的运营商代数的角度来看。我们明确确认的超对称WT身份在连续极限的第一个非平凡的顺序在半微扰扩展。
英文摘要：
We address some issues relating to a supersymmetric (SUSY) Ward-Takahashi (WT) identity in Sugino's lattice formulation of two-dimensional (2D) $\mathcal{N}=(2,2)$ $SU(k)$ supersymmetric Yang-Mills theory (SYM). A perturbative argument shows that the SUSY WT identity in the continuum theory is reproduced in the continuum limit without any operator renormalization/mixing and tuning of lattice parameters. As application of the lattice SUSY WT identity, we show that a prescription for the hamiltonian density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki, is justified also from a perspective of an operator algebra among correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity in the continuum limit to the first nontrivial order in a semi-perturbative expansion.
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