论文标题
2D TQFT和婴儿宇宙
2d TQFT and baby universes
论文作者
论文摘要
在这项工作中，我们扩展了Marolf和Maxfield的2D拓扑引力模型，以作为其大量动作，任何开放/封闭的TQFT服从Atiyah的公理。这些拓扑引力模型的全息二元是具有随机维度的一维拓扑理论的合奏。具体而言，我们发现TQFT Hilbert空间分裂为扇区，在该扇区之间，边界可观察分解的相关因子，并且边界理论的相应扇区从不同的泊松分布中独立选择了尺寸。作为一个特殊情况，我们详细研究了由2D Dijkgraaf-Witten理论的批量动作构建的重力模型，无论有无世界末日的麸皮，以及任意有限的$ g $。该dijkgraaf-witten重力模型的双重偶尔可以解释为1D拓扑理论，其Hilbert Space是$ G $的随机表示，其上述部门被$ G $的不可约表示标记。这些对我们重力模型的全息解释需要从Baby Universe Hilbert Space中投射出负面状态，Marolf和Maxfield通过（仅）（仅）临时解决方案来实现了将非本地边界术语添加到批量动作中的解决方案。为了将其解决方案置于缺陷的TQFT的完全本地框架中，我们将重力模型的边界与非重力（即固定拓扑）区域中的辅助2D TQFT相结合。在此框架中，可以通过引入引力和非重力区域之间的缺陷线来以局部方式来修复负面状态的难度。然后，重力模型在没有重力的开放/闭合TQFT中，在开放/闭合TQFT中的边界条件集合。
In this work, we extend a 2d topological gravity model of Marolf and Maxfield to have as its bulk action any open/closed TQFT obeying Atiyah's axioms. The holographic duals of these topological gravity models are ensembles of 1d topological theories with random dimension. Specifically, we find that the TQFT Hilbert space splits into sectors, between which correlators of boundary observables factorize, and that the corresponding sectors of the boundary theory have dimensions independently chosen from different Poisson distributions. As a special case, we study in detail the gravity model built from the bulk action of 2d Dijkgraaf-Witten theory, with or without end-of-the-world branes, and for arbitrary finite group $G$. The dual of this Dijkgraaf-Witten gravity model can be interpreted as a 1d topological theory whose Hilbert space is a random representation of $G$ and whose aforementioned sectors are labeled by the irreducible representations of $G$. These holographic interpretations of our gravity models require projecting out negative-norm states from the baby universe Hilbert space, which Marolf and Maxfield achieved by the (only seemingly) ad hoc solution of adding a nonlocal boundary term to the bulk action. In order to place their solution in the completely local framework of a TQFT with defects, we couple the boundaries of the gravity model to an auxiliary 2d TQFT in a non-gravitational (i.e. fixed topology) region. In this framework, the difficulty of negative-norm states can be remedied in a local way by the introduction of a defect line between the gravitational and non-gravitational regions. The gravity model is then holographically dual to an ensemble of boundary conditions in an open/closed TQFT without gravity.
