论文标题
Sachdev-ye-Kitaev模型中的欧几里得至洛伦兹虫洞过渡和重力对称性破裂
Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model
论文作者
论文摘要
我们研究了具有复杂耦合和弱点间相互作用的两个站点的Sachdev-ye-Kitaev模型。在低温下，该系统对jackiw-teitelboim重力和物质的欧几里得虫洞是双重的。有趣的是，尽管哈密顿量是非热者，但能量谱对于足够强的地点耦合而变得真实。在重力中，这种复杂到现实的过渡对应于欧几里得到洛伦兹的过渡：对Lorentzian蠕虫孔的重力SL（2，R）对称性的动态恢复，在欧几里得虫洞中损坏至U（1）。我们通过确定对称破坏的顺序参数并匹配绿色功能的振荡模式来显示这一点。在过渡上方，可以继续进行洛伦兹（Lorentzian）签名，并且对永恒的可遍历虫洞是双重的。此外，我们观察到从虫洞到两个黑洞的热相变，并提供了相关物理量的详细匹配。对级别统计的分析表明，在广泛的参数中，动力学在系统的通用性类别中具有量子混乱，随时间逆转不变性。
We study a two-site Sachdev-Ye-Kitaev model with complex couplings and a weak inter-site interaction. At low temperatures, the system is dual to a Euclidean wormhole in Jackiw-Teitelboim gravity plus matter. Interestingly, the energy spectrum becomes real for sufficiently strong inter-site coupling despite the Hamiltonian being non-Hermitian. In gravity, this complex-to-real transition corresponds to a Euclidean-to-Lorentzian transition: a dynamical restoration of the gravitational SL(2,R) symmetry of the Lorentzian wormhole, broken to U(1) in the Euclidean wormhole. We show this by identifying an order parameter for the symmetry breaking and by matching the oscillating patterns of the Green's functions. Above the transition, the system can be continued to Lorentzian signature and is dual to an eternal traversable wormhole. Additionally, we observe a thermal phase transition from the wormhole to two black holes and provide a detailed matching of the associated physical quantities. The analysis of level statistics reveals that in a broad range of parameters the dynamics is quantum chaotic in the universality class of systems with time reversal invariance.
