论文标题
弦理论中的量子纠缠
Quantum Entanglement in String Theory
论文作者
论文摘要
我们使用Orbifold方法在字符串扰动理论中定义了纠缠熵，这是对现场理论中复制方法的弦类似物。为此，我们使用Newton系列在$ n $中进行分析继续以$ \ Mathbb {C}/\ Mathbb {z} _n $锥形空间为单元的orbifolds的分区功能，以所有奇数Integer $ n $而闻名。在十维型IIB字符串的具体示例中，可以明确计算单循环分区函数，并且可以用WeierStrass $ \ wp $函数表示单循环熵作为明显的模块化不变级数。该系列的融合并不明显，但是从基于全息图的物理论点来看，预计将产生有限的答案以及树级的贡献。该方法对其他弦弦压缩和较高的riemann表面具有自然概括。它可以为给定的弦真真空中的所有顺序提供通用熵的模块化定义，这是对热力学第二定律的潜在感兴趣的。
We define entanglement entropy in string perturbation theory using the orbifold method -- a stringy analog of the replica method in field theory. To this end, we use the Newton series to analytically continue in $N$ the partition functions for string orbifolds on $\mathbb{C}/\mathbb{Z}_N$ conical spaces, known for all odd integer $N$. In the concrete example of ten-dimensional Type-IIB strings, the one-loop partition function can be computed explicitly and the one-loop entropy can be expressed as a manifestly modular invariant series in terms of the Weierstrass $\wp$ function. The convergence of the series is not evident but, from physical arguments based on holography, it is expected to yield a finite answer together with the tree level contribution. This method has a natural generalization to other string compactifications and to higher genus Riemann surfaces; it can provide a modular invariant definition of generalized entropy in a given string vacuum to all orders, of potential interest for the generalized second law of thermodynamics.
