从一到八：三维 ${\boldsymbol {\rm N} = 4}$ 超杨-米尔斯理论中的超对称恢复
From One to Eight: Supersymmetry Restoration in Lattice 3D ${\cal N} = 4$ Super Yang--Mills
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中文总结 AI 辅助
本研究推导三维 ${\boldsymbol {\rm N} = 4}$ 超杨-米尔斯理论的额外扭超对称，提出连续极限下旋转对称恢复将自动恢复 ${\boldsymbol R}$-对称，无需微调即可实现完整超对称恢复，为相关三维超对称规范理论的非微扰格点研究奠定基础。
中文摘要 AI 辅助
拓扑扭转为构造超对称规范理论的格点表述提供了有力框架。在三维中，${\boldsymbol {\rm N} = 4}$ 超杨-米尔斯理论的扭版可被离散化，使得在非零格点间距 $a$ 下，一个幂零标量超对称得以精确保留；其余七个超对称则因 ${\boldsymbol {\rm O}(a)}$ 级别的格点人工效应而破缺。一个重要问题是：这些超对称是否会在连续极限 ${\boldsymbol a \to 0}$ 时自动恢复，还是需要对格点耦合进行微调？本研究通过将连续理论的离散 ${\boldsymbol R}$-对称与标量超荷的作用相结合，推导得到了额外的扭超对称。该构造表明，连续极限下旋转对称性的恢复意味着 ${\boldsymbol R}$-对称的恢复，进而无需额外微调即可自动增强为完整的 ${\boldsymbol {\rm N} = 4}$ 超对称。这些结果有望实现对与弦论和镜像对称相关的三维超对称规范理论的非微扰格点研究。
英文摘要
Topological twisting provides a powerful framework for constructing lattice formulations of supersymmetric gauge theories. In three dimensions, a twisted version of ${\cal N} = 4$ super Yang--Mills theory can be discretized so that one nilpotent scalar supersymmetry is preserved exactly at nonzero lattice spacing. The remaining seven supersymmetries are broken by lattice artifacts of ${\cal O}(a)$, where $a$ is the lattice spacing. An important question is whether these supersymmetries are automatically restored in the continuum limit $a \to 0$, or whether fine-tuning of the lattice couplings is required. In this work, we derive the additional twisted supersymmetries by combining discrete $R$-symmetries of the continuum theory with the action of the scalar supercharge. This construction suggests that restoration of rotational symmetry in the continuum limit implies restoration of $R$-symmetry, leading to an automatic enhancement to the full ${\cal N} = 4$ supersymmetry without further tuning. These results may enable nonperturbative lattice studies of three-dimensional supersymmetric gauge theories relevant to string theory and mirror symmetry.
