挤压锥的分布几何
Distributional Geometry of Squashed Cones
摘要：
本文将文献[1]中关于锥奇点流形上积分曲率不变量的正则化方法推广到了压缩锥的情形。一般情况下，压缩圆锥奇点在与奇异曲面$Σ$正交的子空间中不具有旋转O（2）对称性，从而允许曲面具有外曲率.压缩圆锥奇点的一个新特征是积分不变量中的表面项在小角度亏损的极限下也依赖于$Σ$的外曲率。一个例子的不变量，这是二次多项式的黎曼曲率阐述了在不同的维度和应用到几个问题有关的纠缠熵。结果与四维共形理论中纠缠熵的对数项计算结果完全一致。该方法的其他应用包括非共形理论中纠缠熵的对数项和引力场理论中纠缠熵的全息公式。
英文摘要：
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational O(2) symmetry in a subspace orthogonal to a singular surface $Σ$ so that the surface is allowed to have extrinsic curvatures. A new feature of the squashed conical singularities is that the surface terms in the integral invariants, in the limit of small angle deficit, now depend also on the extrinsic curvatures of $Σ$. A case of invariants which are quadratic polynomials of the Riemann curvature is elaborated in different dimensions and applied to several problems related to entanglement entropy. The results are in complete agreement with computations of the logarithmic terms in entanglement entropy of 4D conformal theories [2]. Among other applications of the suggested method are logarithmic terms in entanglement entropy of non-conformal theories and a holographic formula for entanglement entropy in theories with gravity duals.
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