2021/11/09 by Dionysios Anninos, Anninos, Dionysios, Beatrix Mühlmann +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2111.05344
openalex publication_date 2021/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the genus expansion on compact Riemann surfaces of the gravitational path integral Z(m)grav in two spacetime dimensions with cosmological constant Λ>0 coupled to one of the non-unitary minimal models M2m-1,2. In the semiclassical limit, corresponding to large m, Z(m)grav admits a Euclidean saddle for genus h≥ 2. Upon fixing the area of the metric, the path integral admits a round two-sphere saddle for h=0. We show that the OPE coefficients for the minimal weight operators of M2m-1,2 grow exponentially in m at large m. Employing the sewing formula, we use these OPE coefficients to obtain the large m limit of the partition function of M2m-1,2 for genus h≥ 2. Combining these results we arrive at a semiclassical expression for Z(m)grav. Conjecturally, Z(m)grav admits a completion in terms of an integral over large random Hermitian matrices, known as a multicritical matrix integral. This matrix integral is built from an even polynomial potential of order 2m. We obtain explicit expressions for the large m genus expansion of multicritical matrix integrals in the double scaling limit. We compute invariant quantities involving contributions at different genera, both from a matrix as well as a gravity perspective, and establish a link between the two pictures. Inspired by the proposal of Gibbons and Hawking relating the de Sitter entropy to a gravitational path integral, our setup paves a possible path toward a microscopic picture of a two-dimensional de Sitter universe.