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Low-dimensional De Sitter quantum gravity. (English) Zbl 1437.83037

Summary: We study aspects of Jackiw-Teitelboim (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering. Along the way, we show that JT gravity in \(\mathrm{dS}_2\) is an analytic continuation of JT gravity in Euclidean \(\mathrm{ AdS}_2\), and that pure gravity in \(\mathrm{dS}_3\) is a continuation of pure gravity in Euclidean \(\mathrm{AdS}_3\). We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.

MSC:

83C45 Quantization of the gravitational field
83C80 Analogues of general relativity in lower dimensions
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
58J28 Eta-invariants, Chern-Simons invariants
17B68 Virasoro and related algebras

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