Event description
I will discuss a 2d dilaton gravity theory with a sine potential and show this theory has a microscopic holographic realization as the double-scaled SYK model at the disk level. The periodicity of the dilaton potential leads to a Hamiltonian in which the momentum conjugate to the length of two-sided Cauchy slices is periodic and, as a consequence, the length of the ERB in sine dilaton gravity is discrete after gauging this symmetry. For closed cauchy slices, this discretization of the physical Hilbert space corresponds with a discretization of the length of the neck of trumpets. By appropriately gluing two such trumpets together, the wormhole in sine dilaton gravity is computed and matches the spectral correlation of a one-cut matrix integral. This shows that our theory is a path integral formulation of q-deformed JT gravity, where the size of matrices is large but finite. As a result, the topological expansion of sine dilaton gravity goes beyond the realm of DSSYK and potentially captures some features of the full SYK model, which could provide a microscopic holographic description of a cosmological universe.