论文标题
表面缺陷，异常和$ b $ - 淘汰
Surface Defect, Anomalies and $b$-Extremization
论文作者
论文摘要
量子场理论（QFT）在存在缺陷的情况下表现出新型的异常类型，这些异常在约束缺陷动力学和缺陷重新归一化组（RG）流中起重要作用。在这里，我们研究了一般时空维度的保形场理论（CFT）中的表面缺陷及其异常。当缺陷是保形时，它的特征是与2D CFTS的$ c $ - an nomaly类似的保形$ b $ anosomaly。 $ b $ - 理论指出，$ b $必须在缺陷的RG流下单调减少，并通过与虚假的缺陷DILATON耦合证明。我们通过在自由标量理论中明确推导DILATON的有效RG流量来重新审视证明。对于保留$ {\ cal n} =（0,2）$ supersymmetry的共形表面缺陷，我们证明了$ b $ - anomaly与$ u（1）_r $ symmetry的't Hooft异常之间的普遍关系。我们还建立了$ b $ - 发挥原则，该原则标识了$ {\ cal n} =（0,2）$保留RG Flow的SuperCongormal $ u（1）_r $ symmetry。他们共同提供了一种强大的工具，可以提取强烈耦合表面缺陷的$ B $ ano。为了说明我们的方法，我们确定了3D，4D和6D SCFT的许多表面缺陷的$ B $ - andemalies。我们还对缺陷相关功能中这些缺陷保形和'T Hooft异常的表现进行评论。
Quantum field theories (QFT) in the presence of defects exhibit new types of anomalies which play an important role in constraining the defect dynamics and defect renormalization group (RG) flows. Here we study surface defects and their anomalies in conformal field theories (CFT) of general spacetime dimensions. When the defect is conformal, it is characterized by a conformal $b$-anomaly analogous to the $c$-anomaly of 2d CFTs. The $b$-theorem states that $b$ must monotonically decrease under defect RG flows and was proven by coupling to a spurious defect dilaton. We revisit the proof by deriving explicitly the dilaton effective action for defect RG flow in the free scalar theory. For conformal surface defects preserving ${\cal N}=(0,2)$ supersymmetry, we prove a universal relation between the $b$-anomaly and the 't Hooft anomaly for the $U(1)_r$ symmetry. We also establish the $b$-extremization principle that identifies the superconformal $U(1)_r$ symmetry from ${\cal N}=(0,2)$ preserving RG flows. Together they provide a powerful tool to extract the $b$-anomaly of strongly coupled surface defects. To illustrate our method, we determine the $b$-anomalies for a number of surface defects in 3d, 4d and 6d SCFTs. We also comment on manifestations of these defect conformal and 't Hooft anomalies in defect correlation functions.
