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arXiv 2212.03219hep-th
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2+1维闭切片上的全息宇宙学

Holographic Cosmology on Closed Slices in 2+1 Dimensions

Goncalo Araujo-Regado

AI总结:

本文将柯西切片全息应用于Λ>0闭切片上的引力量子化,在CPT对偶分支基中求解Wheeler-DeWitt方程,并推测分支叠加选择与路径积分几何类之间的联系及宇宙量子态的唯一性问题。

摘要:

我们将柯西切片全息框架应用于Λ>0的闭切片上的引力量子化(为具体起见,重点关注2+1维)。我们在CPT对偶分支的基中得到了Wheeler-DeWitt方程的解。每个分支都是一个具有虚中心荷的T²形变共形场论配分函数。我们在纯引力的迷你超空间玩具模型中计算了2+1维的显式解。这一分析为我们提供了证据,以推测分支叠加的选择与引力路径积分中求和的几何类选择之间的联系。我们进一步证明,在闭切片上的完整量子引力中,体幺正性成立,尽管欧几里得全息场论不是反射正定的。基于这一分析,我们对宇宙量子态的(非)唯一性进行了推测。

英文摘要:

We apply the framework of Cauchy Slice Holography to the quantization of gravity on closed slices with $Λ>0$ (with a focus on $2+1$ dimensions for concreteness). We obtain solutions to the Wheeler-DeWitt equation in a basis of CPT-dual branches. Each branch is a $T^2$-deformed CFT partition function with imaginary central charge. We compute explicit solutions in $2+1$ dimensions in a minisuperspace toy model of pure gravity. This analysis gives us evidence to conjecture a connection between the choice of superposition of branches and the choice of class of geometries to sum over in the gravitational path integral. We further show that, in full quantum gravity on closed slices, bulk unitarity holds, despite the Euclidean holographic field theory not being reflection-positive. We conjecture about the (non)uniqueness of the quantum state of the Universe, in light of this analysis.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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