Periodic Dilaton Gravity and q-Deformed JT Gravity

Explore a high-energy theory seminar that delves into dilaton gravity with sine potential, focusing on how periodic shifts of the dilaton are treated as redundancy. Learn about the microscopic holographic realization through the double-scaled SYK model and understand how dilaton periodicity discretizes Cauchy slice lengths. Examine the relationship between trumpet neck length discretization and physical Hilbert space, while discovering how the KG inner product provides positive definite inner product measurements. Investigate the connection between double trumpet and spectral correlation in one-cut matrix integral, demonstrating the theory's role as a path integral formulation of q-deformed JT gravity. Understand why the no-boundary state isn't physical, how the disk represents a sum of physical trumpets with Gaussian wavefunction, and grasp the importance of treating dilaton shift symmetry as redundancy to avoid theoretical inconsistencies and divergent partition functions.