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This project is a study of certain aspects of quantum gravity in two- and three-dimensional de Sitter spaces. The model used in dS2 is the Jackiw-Teitelboim (JT) gravity which involves a scalar (dilaton) coupling. At low-energy limit this model becomes Schwarzian theory for which one can compute one-loop partition function. Along the way, the model is recasted into the first order formalism which helps to find an appropriate measure for the partition function. For two geometries of interest (Hartle-Hawking and generalised dS2) these partition functions are functional integrals over the orbits Diff(S1)/PSL(2, ℝ) and Diff(S1)/U(1). The layout for quantum gravity in dS3 is practically the same and many results appear to be quite similar. Although, there are as many differences. Ultimately, the goal here is somewhat different, namely to determine one-loop correction to the central charge of the theory dual to dS3. This is done by computing one-loop partition functions for dS3 in different coordinates (global and inflating patch). Similarly, these two partition functions are integrals over the orbits Diffℂ(S1)/PSL(2, ℂ) and Diffℂ(S1)/U(1). Additionally, a putative genus expansion for the JT gravity is investigated along with some concrete computations being done for the case of the Hartle-Hawking geometry

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Alexsey Chernichenko, Uppsala University, Sweden
Seminar Room 0.01, ETP
Contact: Dmitry Bagrets