SYK wormholes out of equilibrium

In 2 dimensions, holographic duality gives the possibility of studying quantum gravity in terms of the dual SYK quantum mechanical theory. A particularly capturing model involves two coupled SYK systems. The large N limit is exactly solvable and exhibits phases and revival phenomena consistent with the interpretation as  dual to an eternal traversable wormhole. We will introduce in this system a periodic driving as a means of studying its excitation and relaxation dynamics. We will find resonances at  the conformal spectrum, as well as for the lowest graviton state. Moreover we will shed some light on the status of the elusive hot wormhole phase. Also we compute the Lyapunov exponent and see that it indeed serves as an order parameter across the wormhole-black hole phase transition. The status at finite N is much less understood. The dual ot  traversing the wormhole should lead to a novel type of chaos induced by many body teleportation. I will report on our ongoing work in this direction.