One-dimensional Quantum Gravity and the Schwarzian theory

Abstract

We develop a model of one-dimensional (Conformal) Quantum Gravity. By discussing the connection between Goldstone and Gauge theories, we establish that this model effectively computes the partition function of the Schwarzian theory where the $\text{SL}(2,\mathbb{R})$ symmetry is realized on the base space. The computation is straightforward, involves a local quantum measure and does not rely on localization arguments. Non-localities in the model are exclusively related to the value of fixed gauge invariant moduli. Furthermore, we study the properties of these models when all degrees of freedom are allowed to fluctuate. We discuss the UV finiteness properties of these systems and the emergence of a Planck's length.

arXiv comment18 pages + references; v2: minor modifications in the main text; added references

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Cited by in corpus (3)

• Finite Features of Quantum De Sitter Space
• Interpolating geometries and the stretched dS${}_2$ horizon
• Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields