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arXiv 2208.03334hep-th
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强次可加性之外的全息纠缠熵不等式

Holographic entanglement entropy inequalities beyond strong subadditivity

Lucas Daguerre, Matias Ginzburg, Gonzalo Torroba

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33 pages, 3 figures
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摘要：

量子场论中的真空纠缠熵提供了关于重整化群流的非微扰信息。到目前为止，大多数研究都集中在与偶维时空中的外尔反常有关的普适项和奇维时空中的球自由能$F$上。本文研究了具有引力场的场论在半径为$R$的球上的大半径极限下的纠缠熵。在大半径处，熵可以进行$R$幂的几何展开;主导项是众所周知的面积项，还有次主导项。这些项可以是物理的，它们包含关于完整的重整化群流的信息，并且它们再现了特定情况下已知的单调性定理。利用全息纠缠熵的Hamilton-Jacobi方程，我们建立了一种计算它们的有效方法。我们首先重现了已知的结果，面积项，系数乘以$R^{d-2}$的纠缠熵。然后我们得到了$R^{d-4}$项的全息结果，并建立了它的不可逆性。最后，我们推导了全息理论的$R^{d-6}$系数，并建立了它的不可逆性。这一结果超越了基于强次可加性的量子场论中已经证明的结果，并暗示了在大于4的时空维中分析重整化群单调性的新方法。

英文摘要：

The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time dimensions, and the sphere free energy $F$ in odd dimensions. In this work we study the entanglement entropy on a sphere of radius $R$ in a large radius limit, for field theories with gravity duals. At large radius the entropy admits a geometric expansion in powers of $R$; the leading term is the well-known area term, and there are subleading contributions. These terms can be physical, they contain information about the full renormalization group flow, and they reproduce known monotonicity theorems in particular cases. We set up an efficient method for calculating them using the Hamilton-Jacobi equation for the holographic entanglement entropy. We first reproduce the known result for the area term, the coefficient multiplying $R^{d-2}$ in the entanglement entropy. We then obtain the holographic result for the $R^{d-4}$ term and establish its irreversibility. Finally, we derive the $R^{d-6}$ coefficient for holographic theories, and also establish its irreversibility. This result goes beyond what has been proved in quantum field theory based on strong subadditivity, and hints towards new methods for analyzing the monotonicity of the renormalization group in space-time dimensions bigger than four.

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