String Theory Journal Club

Correlation function of JT gravity could be formulated as the volume of moduli space of Riemann surface where the gravity lives. Mirzakhani’s recursion relation then join the story and give rise to the decomposition of Riemann surface along geodesics. Since Mirzakhani’s recursion is the Eynard’s topological recursion after Fourier transformation, JT gravity can represented as a matrix model, and the correlation function of JT gravity corresponds to the resolvent function in this matrix model. The W_{0,1} and W_{0,2} and the spectral curve, as initial data for topological recursion, could be derived from physics. We will also discuss the topological recursion for both supersymmetric JT gravity. The (arXiv) references are 1907.03363, 1903.11115, 0705.3600, 0601194.