对称乘积轨道中的纠缠与纠缠
Entanglement versus entwinement in symmetric product orbifolds
摘要：
本文研究了二维对称乘积轨道耦合傅里叶变换中规范内部自由度的纠缠熵，该耦合傅里叶变换的结构由缝在一起的$N$链组成，其波函数在排列下是对称的.在早期的工作中，引入了一个相关的概念“缠绕”。在这里，我们把这个系统类似于一个系统的$N$全同粒子。从代数的观点出发，指出了$N$粒子外的$k$上的约化密度矩阵与算子的子代数无关，而是与线性子空间有关，并说明了这是充分的.在orbifold CFT中，我们计算了D1/D5系统中与锥形缺陷几何或无质量BTZ黑洞全息对偶的单链的熵，得到了与纠缠完全相同的结果.我们还计算了两股在代表锥形缺陷的状态下的熵;结果与纠缠不同。在这种情况下，匹配纠缠需要找到一种规范不变的方式来在链之间施加连续性。
英文摘要：
We study the entanglement entropy of gauged internal degrees of freedom in a two dimensional symmetric product orbifold CFT, whose configurations consist of $N$ strands sewn together into "long" strings, with wavefunctions symmetrized under permutations. In earlier work a related notion of "entwinement" was introduced. Here we treat this system analogously to a system of $N$ identical particles. From an algebraic point of view, we point out that the reduced density matrix on $k$ out of $N$ particles is not associated with a subalgebra of operators, but rather with a linear subspace, which we explain is sufficient. In the orbifold CFT, we compute the entropy of a single strand in states holographically dual in the D1/D5 system to a conical defect geometry or a massless BTZ black hole and find a result identical to entwinement. We also calculate the entropy of two strands in the state that represents the conical defect; the result differs from entwinement. In this case, matching entwinement would require finding a gauge-invariant way to impose continuity across strands.
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