论文标题
2D超符号缺陷的中央费用
Central Charges of 2d Superconformal Defects
论文作者
论文摘要
在维度$ d> 3 $的共形场理论（CFT）中，二维（2D）保形缺陷的一部分是由缺陷对痕量异常的贡献定义的中心电荷来表征的。但是，通常很难计算这些中心电荷的CFT。对于SuperSymmetric（SUSY）CFTS（SCFTS）中的SuperConformal 2D缺陷，我们展示了如何在$ s^2 $上沿$ s^d $上的$ S^d $计算这些缺陷的中心费用，或者在$ s^2 $上或$ s^1 \ s^1 \ s^1 \ times S^{d-1} $沿着$ s^1^1^1 \ times s^times s^1 $。在后一种情况下，我们建议将缺陷中心电荷出现在总体归一化因子中，这是Susy Casimir能量的一部分。对于4d $ {\ MATHCAL N} = 2 $ scfts的2D半BP缺陷，在6d $ {\ Mathcal n} =（2,0）$ scft中，我们获得了新颖的，使用SUSY本地化的分区功能的现有结果的缺陷中心指控，用于SUSY本地化，Susy Indices，以及对2D liouer，$ qulious youry，y y y y y y y y和quly y y-q $ qda和q. $ qda和quly y-q $ - 我们的一些缺陷中心收费结果与先前通过全息图获得的结果一致，这表明后者不仅是$ n $和/或强耦合限制，而且是准确的。我们的方法可以直接扩展到其他各种编纂的其他超符号缺陷，因为我们在6D $ {\ Mathcal n} =（2,0）$ scft中证明了4D缺陷。
In conformal field theories (CFTs) of dimension $d>3$, two-dimensional (2d) conformal defects are characterised in part by central charges defined via the defect's contribution to the trace anomaly. However, in general for interacting CFTs these central charges are difficult to calculate. For superconformal 2d defects in supersymmetric (SUSY) CFTs (SCFTs), we show how to compute these defect central charges from the SUSY partition function either on $S^d$ with defect along $S^2$, or on $S^1 \times S^{d-1}$ with defect along $S^1 \times S^1$. In the latter case we propose that defect central charges appear in an overall normalisation factor, as part of the SUSY Casimir energy. For 2d half-BPS defects in 4d ${\mathcal N}=2$ SCFTs and in the 6d ${\mathcal N}=(2,0)$ SCFT we obtain novel, exact results for defect central charges using existing results for partition functions computed using SUSY localisation, SUSY indices, and correspondences to 2d Liouville, Toda, and $q$-deformed Yang-Mills theories. Some of our results for defect central charges agree with those obtained previously via holography, showing that the latter are not just large-$N$ and/or strong-coupling limits, but are exact. Our methods can be straightforwardly extended to other superconformal defects, of various codimension, as we demonstrate for a 4d defect in the 6d ${\mathcal N}=(2,0)$ SCFT.
