Quantum gravity from timelike Liouville [Quantum Spacetime Seminar]

A proper definition of the path integral of quantum gravity has been a long standing puzzle because the conformal factor of the Euclidean metric has a wrong-sign kinetic term.  We propose a definition of two-dimensional quantum gravity with  cosmological constant using conformal bootstrap for the timelike Liouville theory coupled to supercritical matter.  We prove a no-ghost theorem for the states in the BRST cohomology. We show  that the four point function constructed by gluing  the timelike DOZZ three point functions  is well-defined and  crossing symmetric with the choice of the Ribault-Santachiara contour for the internal momenta but with external momenta corresponding to physical  states in the BRST cohomology.