Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermitian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly at finite temperature real black holes solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.

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非厄密全息

量子理论可以用某些非埃尔米特哈密顿量来表示。PT表示的反线性对合就是这种哈密顿量的对称性。在PT对称状态下，非Hermitian哈密顿量通过Hermitian相似变换与Hermitian关联。我们将非Hermitian量子理论的概念扩展到规范重力对偶。非渐近性是通过边界条件在渐近AdS时空中引入的。在零温度下，PT相变被识别为溶液不再是真实的点。出乎意料的是，在有限的温度下，可以在准赫米特制度之外找到真正的黑洞解决方案。然而，这些背景对于波动是不稳定的，所述波动建立了在有限温度下PT相变的全息对偶的持久性。