单曲面上外尔费米子的格点表述
A lattice formulation of Weyl fermions on a single curved surface
AI总结：
本研究探究3D正方晶格上畴壁为2D球面的单畴壁费米子系统，发现自由理论下单个Weyl费米子局域于畴壁并感受引力，含非平凡U(1)规范场时出现相反手性零模导致低能理论为类矢量，还讨论了构建格点手征规范理论的障碍规避方法。
摘要：
在标准的格点畴壁费米子表述中，需要两个平面畴壁，左、右手无质量模式均会在其上出现。本研究探究了具有非平凡弯曲背景的单畴壁系统，具体研究了3D正方晶格上的有质量费米子，其畴壁为2D球面。在自由理论中，我们发现单个外尔（Weyl）费米子局域在畴壁上，并通过诱导自旋联络感受到引力。然而，当存在拓扑非平凡的U(1)链规范场时，我们发现一个具有相反手性的零模局域在规范场奇异的中心位置。在后一种情况下，低能有效理论并非手性的，而是类矢量的。我们讨论了如何在单畴壁费米子系统中构建格点手征规范理论时规避这一障碍。
英文摘要：
In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a $3D$ square lattice, whose domain-wall is a $2D$ sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.
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