论文标题
二维纯超对称理论的注释
Notes on two-dimensional pure supersymmetric gauge theories
论文作者
论文摘要
In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/Z_k, SO(2k)/Z_2, Sp(2k)/Z_2, E_6/Z_3, and E_7/Z_2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification始于以前的工作。在每种情况下，我们都会发现，对于离散的theta角度的一个值，都有一个超对称性真空吸尘器，并且对于其他值，没有超对称性真空吸尘器，因此，对于大多数离散的theta角度，IR中的超对称性都会在IR中损坏。此外，对于超对称性不间断的离散theta角度的一个杰出值，该理论在IR中具有许多扭曲的手性多重自由度与等级。我们借此机会进一步开发了非亚伯镜的技术，讨论了镜像与G仪理论的镜子如何从镜像到G/k的g/k仪表理论，k的k个中心的一个子组。特别是，在这些情况下，离散的theta角度比以前的论文中所研究的纯粹的理论更为复杂，因此我们讨论了这些复杂的研究，因此这些纯粹的理论的实现了这些复杂的研究。我们发现，在原始仪表理论及其镜子中，离散的theta角度与root sublattices的权重晶格的商的描述密切相关。我们执行了许多一致性检查，将结果与基本群体理论关系以及分解性进行了比较，该结果描述了如何将具有单一形式的对称性（例如具有非平凡中心的纯度规定理论）分解为脱节工会的二维理论，在这种情况下是具有有限的规格组和离散的theta Angles的纯理论。
In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/Z_k, SO(2k)/Z_2, Sp(2k)/Z_2, E_6/Z_3, and E_7/Z_2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification begun in previous work. We find in each case that there are supersymmetric vacua for precisely one value of the discrete theta angle, and no supersymmetric vacua for other values, hence supersymmetry is broken in the IR for most discrete theta angles. Furthermore, for the one distinguished value of the discrete theta angle for which supersymmetry is unbroken, the theory has as many twisted chiral multiplet degrees of freedom in the IR as the rank. We take this opportunity to further develop the technology of nonabelian mirrors to discuss how the mirror to a G gauge theory differs from the mirror to a G/K gauge theory for K a subgroup of the center of G. In particular, the discrete theta angles in these cases are considerably more intricate than those of the pure gauge theories studied in previous papers, so we discuss the realization of these more complex discrete theta angles in the mirror construction. We find that discrete theta angles, both in the original gauge theory and their mirrors, are intimately related to the descriptions of centers of universal covering groups as quotients of weight lattices by root sublattices. We perform numerous consistency checks, comparing results against basic group-theoretic relations as well as with decomposition, which describes how two-dimensional theories with one-form symmetries (such as pure gauge theories with nontrivial centers) decompose into disjoint unions, in this case of pure gauge theories with quotiented gauge groups and discrete theta angles.
