论文标题
自由标量的反射熵
Reflected entropy for free scalars
论文作者
论文摘要
我们继续研究高斯系统的反射熵（a，b）$。在本文中，我们提供的一般公式在任意维度中对自由标量字段有效。与费米子情况类似，由此产生的表达式是根据田地相关因子充分确定的，这使得它们可与晶格计算。我们将其应用于$（1+1）$ - 尺寸手性标量的情况下，其反射熵我们在两个间隔中计算为交叉比例的函数，并将其与以前的全息图和自由屈光度的结果进行了比较。对于两种类型的免费理论，我们都会发现反射熵都满足了猜想的单调属性$ r（a，bc）\ geq r（a，b）$。然后，我们将其移至$（2+1）$尺寸，并将其用于平方区域的自由标量，费米和全息图，确定了非常近的和非常紧密的状态，并将其与它们的共同信息对应物进行了比较。在所有情况下，均以$（1+1）$ - 和$（2+1）$ - 尺寸理论的理论，我们验证是否满足了两种数量的一般不平等，$ r（a，b）\ geq I（a，b）$都可以满足。我们的结果表明，对于以长度尺度为特征的一般区域，$ l_a \ sim l_b \ sim l $，并分开了一个距离$ \ ell $，这是大分离体制中的反射熵（$ x \ equiv l/equiv l/\ eeld \ ell \ ll 1 $）的行为作为$ r（x）\ sim-im-i（x）\ sim- i（x）\ sim-i（x）\ i（x）\ i（x）\ logency cfts cfts cfts cfts cfts。
We continue our study of reflected entropy, $R(A,B)$, for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a $(1+1)$-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property $R(A,BC) \geq R(A,B)$. Then, we move to $(2+1)$ dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for $(1+1)$- and $(2+1)$-dimensional theories, we verify that the general inequality relating both quantities, $R(A,B)\geq I(A,B)$, is satisfied. Our results suggest that for general regions characterized by length-scales $L_A\sim L_B\sim L$ and separated a distance $\ell$, the reflected entropy in the large-separation regime ($x\equiv L/\ell \ll 1$) behaves as $R(x) \sim - I(x) \log x$ for general CFTs in arbitrary dimensions.
