标题： 关于非共形N=2规范理论中的BPS威尔逊回路和局部化的注记 显示英文标题

标题： Remarks on BPS Wilson loops in non-conformal N=2 gauge theories and localization

摘要： 我们考虑四维 N=2 SU(N) 超对称杨-米尔斯理论中的 1/2 BPS 超对称圆形威尔逊圈，这些理论具有无质量物质内容且 β 函数非零。遵循佩斯图恩的方法，只要一阶行列式能够一致正则化，我们可以利用球面 S4 上的超对称局域化将这些可观测量映射到一个矩阵模型。采用适当的过程，我们构建了这些理论的正则化矩阵模型，并表明在 g^4 阶，1/2 BPS 威尔逊圈的预测与基于直接计算 S4 上费曼图的标准微扰重整化一致。尽管在量子水平上共形对称性被破坏，我们还证明了在这个微扰阶数下，矩阵模型方法完美捕捉到了平坦空间中重整化可观测量的表达式。此外，我们详细重新审视了差异理论方法，表明当 β 函数非零时，这种方法未能解释由重整化程序使其有限的消失项，并且这些项参与了 g^6 阶的修正。 显示英文摘要

摘要： We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional N=2 SU(N) SYM theories with massless matter content and non-vanishing beta-function. Following Pestun's approach, we can use supersymmetric localization on the sphere S4 to map these observables into a matrix model, provided that the one-loop determinants are consistently regularized. Employing a suitable procedure, we construct the regularized matrix model for these theories and show that, at order g^4, the predictions for the 1/2 BPS Wilson loop match standard perturbative renormalization based on the direct evaluation of Feynman diagrams on S4. Despite conformal symmetry begin broken at the quantum level, we also demonstrate that the matrix model approaches perfectly captures the expression of the renormalized observable in flat space at this perturbative order. Moreover, we revisit in detail the difference theory approach, showing that when the beta-function is non-vanishing, this method does not account for evanescent terms which are made finite by the renormalization procedure and participate to the corrections at order g^6.