论文标题
游离费米子循环/对称的Orbifold CFT和纠缠熵
Free Fermion Cyclic/Symmetric Orbifold CFTs and Entanglement Entropy
论文作者
论文摘要
在本文中，我们研究了由循环和对称的dirac fermions的循环和对称孔定义的二维CFT的性能，尤其是通过关注分区函数和纠缠熵。通过玻体化，我们构造了扭曲操作员，该扭曲算子粘合了两个复杂的平面，以计算Z_2 Orbifold CFT在圆环上的分区函数。我们还通过Hecke操作员发现了Zn Cyclic Orbifold的表达，该表达式提供了循环孔的分区函数与对称的分区函数之间的明确关系。我们计算有限温度状态和量子淬灭的时间依赖性状态的圆圈中的圆环熵和Renyi熵。我们发现，由于具有不同边界条件的复制品的贡献，复制方法计算是高度不平凡的和新的。我们找到了Z_2 Orbifold的完整表达式，并表明周期性加倍。最后，我们讨论了我们关于对称Orbifold CFT的纠缠熵的扩展，并对全息CFT进行了启发式论证。
In this paper we study the properties of two-dimensional CFTs defined by cyclic and symmetric orbifolds of free Dirac fermions, especially by focusing on the partition function and entanglement entropy. Via the bosonization, we construct the twist operators which glue two complex planes to calculate the partition function of Z_2 orbifold CFT on a torus. We also find an expression of Z_N cyclic orbifold in terms of Hecke operators, which provides an explicit relation between the partition functions of cyclic orbifolds and those of symmetric ones. We compute the entanglement entropy and Renyi entropy in cyclic orbifolds on a circle both for finite temperature states and for time-dependent states under quantum quenches. We find that the replica method calculation is highly non-trivial and new because of the contributions from replicas with different boundary conditions. We find the full expression for the Z_2 orbifold and show that the periodicity gets doubled. Finally, we discuss extensions of our results on entanglement entropy to symmetric orbifold CFTs and make a heuristic argument towards holographic CFTs.
