发表机构
Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理研究所与物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将尖点反常维数推广到含平面共形边界/界面的带尖点线缺陷，通过反射正性推导对数项系数的正性约束，在弱耦合理论和全息强耦合理论中验证约束并发现相变及与纠缠熵的关联。
AI 中文摘要
尖点反常维数是带尖点的线缺陷自由能的普适对数贡献，是表征缺陷动力学的有用可观测量。我们将这一概念推广到存在平面共形边界或界面时的带尖点线缺陷，其几何由三个角度以及尖点与边界/界面的距离表征，该距离区分短程和长程区域。所得自由能包含两个大对数项：由常规真空尖点反常维数决定的短程贡献，以及对边界或界面敏感的新长程贡献。利用缺陷射线横向形变的反射正性，我们推导出这些对数项系数的若干约束，可表述为其角海森矩阵的半负定性质，还推导出这些系数延拓到洛伦兹运动学的约束。我们在自由标量理论、麦克斯韦理论以及平面N=4超杨-米尔斯理论的弱耦合极限下，针对不同边界条件计算了这些系数并显式验证了约束。在强耦合下，我们在全息D3-D5缺陷CFT中计算了对数系数，发现由尖点相对于界面的几何驱动的竞争弦世界面之间存在类Gross-Ooguri相变，还观察到该设置下尖点自由能与全息角落纠缠熵存在密切关联。
英文摘要
The cusp anomalous dimension is the universal logarithmic contribution to the free energy of a line defect with a cusp, and provides a useful observable characterizing defect dynamics. We generalize this notion to cusped line defects in the presence of a planar conformal boundary or interface. The geometry is characterized by three angles, and the distance of the cusp from the boundary or interface which separates short-distance and long-distance regimes. The resulting free energy contains two large logarithmic terms: a short-distance contribution governed by the usual vacuum cusp anomalous dimension, and a new long-distance contribution sensitive to the boundary or interface. Using reflection positivity for transverse deformations of the defect rays, we derive several constraints on the coefficients of these logarithmic terms, which can be packaged into negative semi-definiteness of their angular Hessians. We also derive constraints on the continuation of these coefficients to Lorentzian kinematics. We compute these coefficients and verify the constraints explicitly in free scalar and Maxwell theories and in planar $\mathcal N=4$ super-Yang-Mills theory at weak coupling for various choices of boundary conditions. At strong coupling, we compute the logarithmic coefficients in the holographic D3-D5 defect CFT and find a Gross-Ooguri-like phase transition between competing string worldsheets driven by the geometry of the cusp relative to the interface. We also observe a close connection of the cusp free energy in this setup with holographic corner entanglement entropy.
Comments51 pages
