arXiv 1902.050582019-02-25hep-th

奇异曲面纠缠熵的相关微扰

Relevant perturbation of entanglement entropy of singular surfaces

Mostafa Ghasemi, Shahrokh Parvizi

备注：: 46 pages; v2: Errors fixed, Refs. added

摘要：

利用AdS/CFT对应，研究了由给定的CFT的相关微扰导出的奇异边界区域的理论的纠缠熵.在光滑情况下，众所周知的是，通过具有标度维数$Δ=\frac{d+2}{2}$的相关算子对边界理论的相关变形产生了对纠缠熵的对数普适项。作为光滑情形，当边界CFT被相应的算符变形时，我们发现奇异表面的纠缠熵也包含了一个新的对数项，这是由于共形场论的相应微扰引起的，并且依赖于相应算符的标度维数.我们还发现，对于扩展的奇异曲面，$c_{n}\times R^{m}$，以及对数项，新的通用双对数项可能会出现依赖于相关运营商的标度维数和时空维数。这些新项是由于边界理论的相关扰动。

英文摘要：

We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant deformation of the boundary theory by the relevant operator with scaling dimension $Δ=\frac{d+2}{2}$ generates a logarithmic universal term to the entanglement entropy. As the smooth case, when the boundary CFT deformed by a relevant operator, we find that the entanglement entropy of singular surface also contains a new logarithmic term which is due to relevant perturbation of the conformal field theory, and depends on the scaling dimension of relevant operator. We also find for extended singular surfaces, $c_{n}\times R^{m}$, as well as logarithmic term, the new universal double logarithmic terms may appear depending on the scaling dimension of relevant operator and spacetime dimensions. These new terms are due to relevant perturbation of the boundary theory.

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