论文标题
旋转结构和婴儿宇宙
Spin structures and baby universes
论文作者
论文摘要
我们将重力路径积分的2D拓扑模型扩展到包括自旋结构的总和，对应于费米子的Neveu-Schwarz（NS）或Ramond（R）边界条件。当R边界数奇怪时，欧几里得路径积分消失。该路径积分对应于非平凡的婴儿宇宙希尔伯特空间上边界创建算子的相关器。非物质化需要根据分区函数（与NS边界相关的）和Witten指数（与R边界相关的）对整体组成部分进行双重解释，并在具有不同的Hilbert空间维度和不同数量的Bosonic和Fermionic状态的理论集合上进行平均。我们还考虑了一个具有世界末日（EOW）Branes的模型：双重合奏，然后包括随机选择的费米子和玻色子状态的总和。我们提出了两种对批量路径积分的修改，这些修改恢复了单个双重理论中的解释：（i）几何处方，其中我们在其自旋结构上添加了额外的界限，以及（ii）涉及“ Spacetime d-branes”的代数处方。我们将思想扩展到了杰基特尔鲍尔（Jackiw-teitelboim）的重力，并提出了一个单一统一理论的双重描述，该理论在具有本征脑的系统中具有旋转结构。
We extend a 2d topological model of the gravitational path integral to include sums over spin structure, corresponding to Neveu-Schwarz (NS) or Ramond (R) boundary conditions for fermions. The Euclidean path integral vanishes when the number of R boundaries is odd. This path integral corresponds to a correlator of boundary creation operators on a non-trivial baby universe Hilbert space. The non-factorization necessitates a dual interpretation of the bulk path integral in terms of a product of partition functions (associated to NS boundaries) and Witten indices (associated to R boundaries), averaged over an ensemble of theories with varying Hilbert space dimension and different numbers of bosonic and fermionic states. We also consider a model with End-of-the-World (EOW) branes: the dual ensemble then includes a sum over randomly chosen fermionic and bosonic states. We propose two modifications of the bulk path integral which restore an interpretation in a single dual theory: (i) a geometric prescription where we add extra boundaries with a sum over their spin structures, and (ii) an algebraic prescription involving "spacetime D-branes". We extend our ideas to Jackiw-Teitelboim gravity, and propose a dual description of a single unitary theory with spin structure in a system with eigenbranes.
