arXiv 1406.45452014-06-17hep-th

相互作用量子场论零面上的熵与Bousso界

Entropy on a null surface for interacting quantum field theories and the Bousso bound

Raphael Bousso, Horacio Casini, Zachary Fisher, Juan Maldacena

备注：: 35 pages, 6 figures
发表信息：: Phys. Rev. D 91, 084030 (2015)
DOI：: 10.1103/PhysRevD.91.084030

摘要：

研究零平面上线段的真空减冯诺伊曼熵。我们认为，在二维以上的相互作用的量子场论，这个熵有一个简单的表达式在零区间上的应力张量的零分量的期望值。更明确地说，是$ΔS = 2π\int d^{d-2}y \int_0^1 dx^+\, g(x^+)\, \langle T_{++}\rangle$，其中$g(x^+)$是一个依赖于理论的函数。该函数受量子相对熵的一般性质的约束。这些约束条件足以将我们最近关于量子Bousso束缚的自由场证明推广到相互作用的情形。这种将熵作为算子期望值的不寻常表达式意味着熵等于模哈密顿量$ΔS = \langle ΔK \rangle $，其中$K$是右边的算子。我们解释了这个等式如何与$ΔS$的非零值兼容。最后，我们还明确计算函数$g(x^+)$的理论，有一个重力对偶。

英文摘要：

We study the vacuum-subtracted von Neumann entropy of a segment on a null plane. We argue that for interacting quantum field theories in more than two dimensions, this entropy has a simple expression in terms of the expectation value of the null components of the stress tensor on the null interval. More explicitly $ΔS = 2π\int d^{d-2}y \int_0^1 dx^+\, g(x^+)\, \langle T_{++}\rangle$, where $g(x^+)$ is a theory-dependent function. This function is constrained by general properties of quantum relative entropy. These constraints are enough to extend our recent free field proof of the quantum Bousso bound to the interacting case. This unusual expression for the entropy as the expectation value of an operator implies that the entropy is equal to the modular Hamiltonian, $ΔS = \langle ΔK \rangle $, where $K$ is the operator in the right hand side. We explain how this equality is compatible with a non-zero value for $ΔS$. Finally, we also compute explicitly the function $g(x^+)$ for theories that have a gravity dual.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文