Henry Lin (Stanford) “The bulk Hilbert space of double scaled SYK”

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How does the bulk Hilbert space of quantum gravity emerge from a boundary theory? I take up this question in the context of the SYK model in the double scaling limit. Berkooz et. al computed correlation functions in this model by summing chord diagrams. By slicing open these chord diagrams, I will explicitly construct the bulk Hilbert space; it resembles that of a lattice field theory where the length of the lattice is dynamical and determined by the chord number. Under a calculable bulk-to-boundary map, states of fixed chord number map to particular entangled 2-sided states with a corresponding size. This bulk reconstruction is well-defined even when quantum gravity effects are important. Acting on the double scaled Hilbert space is a Type II_1 algebra of observables, which includes the Hamiltonian and matter operators. In the appropriate quantum Schwarzian limit, we also identify the JT gravitational algebra including the physical SL(2,R) symmetry generators, and obtain explicit representations of the algebra using chord diagram techniques.