论文标题
全息纠缠熵不平等超出强度较强的不平等现象
Holographic entanglement entropy inequalities beyond strong subadditivity
论文作者
论文摘要
量子场理论中的真空纠缠熵提供了有关重新归一化组流的非扰动信息。到目前为止，大多数研究都集中在通用术语上，该术语与偶数时空维度和奇数方面的Sphere Free Energy $ f $有关。在这项工作中，我们研究了带有重力双重的野外理论，在半径限制的半径$ r $范围内的纠缠熵。在整个半径上，熵承认$ r $的几何扩展；主词是众所周知的区域术语，并且有超级贡献的贡献。这些术语可以是物理的，它们包含有关完整重新归一化组流量的信息，并且在特定情况下会重现已知的单调性定理。我们设置了一种有效的方法，用于使用汉密尔顿 - 雅各比方程进行全息纠缠熵来计算它们。我们首先重现该区域项的已知结果，该系数在纠缠熵中乘以$ r^{d-2} $。然后，我们获得了$ r^{d-4} $项的全息结果，并确定其不可逆性。最后，我们得出了全息理论的$ r^{d-6} $系数，并确定其不可逆性。该结果远远超出了基于强大的亚热性中量子场理论证明的结果，并暗示了在时空维度大于四个的时期中分析重新归一化组的单调性的新方法。
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.
