论文标题
集体领域理论中纠缠熵的有限性
Finiteness of Entanglement Entropy in Collective Field Theory
论文作者
论文摘要
我们探讨了引力理论中纠缠熵的有限性问题，其新兴空间是全息偶的目标空间。在二维非关键字符串理论和$ c = 1 $矩阵模型的二元性二元性中，该问题已在特征值的空间中使用费米子多体理论进行了研究。特征值空间的子区域的纠缠熵（矩阵模型中的目标空间纠缠）是有限的，其比例由局部费米动量提供。然而，Fermi动量是依赖位置的弦耦合的，正如集体场理论公式中很明显的那样。这表明有限性是一种非扰动效应。我们通过具有消失潜力的基质量子力学的集体田地理论的明确计算为这种期望提供了证据。纠缠熵的累积膨胀的主要术语是使用集体哈密顿量的精确本征和特征值计算得出的，从而获得了有限的结果，并与费米昂答案确切一致。通过扰动地处理理论，我们表明扰动扩展中的每个术语都是紫外线分歧。但是，该系列可以重新定位，从而产生确切的有限结果。我们的结果表明，较高维弦理论的纠缠熵的有限性也是非扰动性的，牛顿常数提供了规模。
We explore the question of finiteness of the entanglement entropy in gravitational theories whose emergent space is the target space of a holographic dual. In the well studied duality of two-dimensional non-critical string theory and $c=1$ matrix model, this question has been studied earlier using fermionic many-body theory in the space of eigenvalues. The entanglement entropy of a subregion of the eigenvalue space, which is the target space entanglement in the matrix model, is finite, with the scale being provided by the local Fermi momentum. The Fermi momentum is, however, a position-dependent string coupling, as is clear in the collective field theory formulation. This suggests that the finiteness is a non-perturbative effect. We provide evidence for this expectation by an explicit calculation in the collective field theory of matrix quantum mechanics with vanishing potential. The leading term in the cumulant expansion of the entanglement entropy is calculated using exact eigenstates and eigenvalues of the collective Hamiltonian, yielding a finite result, in precise agreement with the fermion answer. Treating the theory perturbatively, we show that each term in the perturbation expansion is UV divergent. However the series can be resummed, yielding the exact finite result. Our results indicate that the finiteness of the entanglement entropy for higher dimensional string theories is non-perturbative as well, with the scale provided by the Newton constant.
