Late time saturation of the Einstein-Rosen bridge dual to the Double Scaled SYK model

In this talk I will explain how the size of the Einstein-Rosen (ER) bridge dual to the Double Scaled SYK (DSSYK) model saturates at late times because of finiteness of the underlying quantum Hilbert space.  I will extend recent work implying that the ER bridge size equals the spread complexity of the dual DSSYK theory with an appropriate initial state.  This work shows that the auxiliary "chord basis'' used to solve the DSSYK theory is the physical Krylov basis of the spreading quantum state.  The ER bridge saturation follows from the vanishing of the Lanczos spectrum, derived by methods from Random Matrix Theory (RMT).