自由标量的立方三面角纠缠
Cubic trihedral corner entanglement for a free scalar
摘要：
我们计算了无质量自由标量在3+1维纠缠区边界上立方三面角对$α$ -Renyi熵的普适贡献。普适数$v_α$表现为在缠结区域的大小上为对数的缩放项的系数。我们的数值计算发现，这个通用系数既有较大的幅度和相反的符号，诱导一个光滑的球形纠缠边界在3+1维，其中有一个众所周知的subleading对数标度。尽管存在这些差异，但由于我们有限尺寸晶格计算的不确定性，三面体系数$v_α$对雷尼指数$α$的函数依赖性与球的函数依赖性是不可区分的，球的函数依赖性是对无质量自由标量的解析已知的。我们评论的可能来源，这种$α$依赖性所产生的一般结构的（3+1）维共形场论，并建议计算过去的自由标量，可以进一步阐明的一般结构的三面体发散的雷尼熵。
英文摘要：
We calculate the universal contribution to the $α$-Renyi entropy from a cubic trihedral corner in the boundary of the entangling region in 3+1 dimensions for a massless free scalar. The universal number, $v_α$, is manifest as the coefficient of a scaling term that is logarithmic in the size of the entangling region. Our numerical calculations find that this universal coefficient has both larger magnitude and the opposite sign to that induced by a smooth spherical entangling boundary in 3+1 dimensions, for which there is a well-known subleading logarithmic scaling. Despite these differences, up to the uncertainty of our finite-size lattice calculations, the functional dependence of the trihedral coefficient $v_α$ on the Rényi index $α$ is indistinguishable from that for a sphere, which is known analytically for a massless free scalar. We comment on the possible source of this $α$-dependence arising from the general structure of (3+1)-dimensional conformal field theories, and suggest calculations past the free scalar which could further illuminate the general structure of the trihedral divergence in the Rényi entropy.
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