空心锥和香蕉形区域的全息纠缠熵
Holographic entanglement entropy for hollow cones and banana shaped regions
摘要：
我们考虑香蕉形区域作为紧区域的例子，其边界具有两个圆锥形奇点。它们的正则化全息熵是用所有发散项和有限项计算的。对数发散的平方系数，也在这种情况下，内部弯曲的边界，同意在文献中计算的无限圆锥与其内部平坦的边界。对于其他共形不变系数的普通对数发散异常下的共形变换观察。锥的纠缠熵所需的最小子流形的构造需要对柯西数据进行微调。这种微调的扰动导致解决方案相关的空心锥。计算了空心锥的纠缠熵的发散部分。增加它们的外边界和内边界的开度角之间的差异，人们发现小差异的连通解到大差异的断开解之间的过渡。
英文摘要：
We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared logarithmic divergence, also in such a case with internally curved boundary, agrees with that calculated in the literature for infinite circular cones with their internally flat boundary. For the otherwise conformally invariant coefficient of the ordinary logarithmic divergence an anomaly under exceptional conformal transformations is observed. The construction of minimal submanifolds, needed for the entanglement entropy of cones, requires fine-tuning of Cauchy data. Perturbations of such fine-tuning leads to solutions relevant for hollow cones. The divergent parts for the entanglement entropy of hollow cones are calculated. Increasing the difference between the opening angles of their outer and inner boundary, one finds a transition between connected solutions for small differences to disconnected solutions for larger ones.
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