论文标题
AD/CFT中的浆果阶段,虫洞和分解
Berry phases, wormholes and factorization in AdS/CFT
论文作者
论文摘要
对于二维全息CFT,我们证明了浆果相对于将希尔伯特空间与蠕虫的存在无关紧要的作用。虫洞的特征是非脱落形式,引起浆果相。对于在引力空间中连接两个间距区域的虫洞,我们发现非表演度与边界CFT相位空间中出现的变量有关。该变量对应于整体中的循环积分。通过这个循环积分,在双重纠缠的CFT中显而易见的非事实化变得显而易见。此外,我们根据所涉及的双重散装差异类型对全息CFT中的浆果阶段进行分类。我们区分Virasoro,Gauge和模块化浆果阶段,每个相都对应于整体中的时空虫孔的几何形状。使用运动学空间,我们将模块化哈密顿量与浆果曲率之间的关系扩展到有限的温度情况。我们发现,克罗夫顿形式给出的浆果曲率表征了在黑洞存在下纠缠熵的拓扑过渡。
For two-dimensional holographic CFTs, we demonstrate the role of Berry phases for relating the non-factorization of the Hilbert space to the presence of wormholes. The wormholes are characterized by a non-exact symplectic form that gives rise to the Berry phase. For wormholes connecting two spacelike regions in gravitational spacetimes, we find that the non-exactness is linked to a variable appearing in the phase space of the boundary CFT. This variable corresponds to a loop integral in the bulk. Through this loop integral, non-factorization becomes apparent in the dual entangled CFTs. Furthermore, we classify Berry phases in holographic CFTs based on the type of dual bulk diffeomorphism involved. We distinguish between Virasoro, gauge and modular Berry phases, each corresponding to a spacetime wormhole geometry in the bulk. Using kinematic space, we extend a relation between the modular Hamiltonian and the Berry curvature to the finite temperature case. We find that the Berry curvature, given by the Crofton form, characterizes the topological transition of the entanglement entropy in presence of a black hole.