Real-time methods in JT/SYK holography

We study the conventional holographic recipes and its real-time extensions in the context of the correspondence between Sachdev–Ye–Kitaev quantum mechanics and JT gravity. We first observe that only closed contours are allowed to have a 2d space-time holographic dual and standard holographic formulas. Thus, in a real-time formulation of the duality, the boundaries of a classical connected geometry are a set of closed curves, parameterized by a complex time contour as in the Schwinger–Keldysh framework. In this context, a consistent extension of the standard holographic formulas can be proposed, describing the (real-time) correspondence between gravity and boundary quantum models that include averaging on the coupling constants. We investigate the proposed prescription in different AdS solutions with Schwinger–Keldysh boundary condition, dual to a boundary quantum theory at finite temperature defined on a complex time contour, and consider also classical, asymptotically AdS solutions (wormholes) with two disconnected boundaries. In doing this, we revisit the so-called factorization problem, and its resolution in conventional holography by virtue of some (non-local) coupling between disconnected boundaries, and we show how in specific contexts, the averaging proposal by-passes the paradox as well, since it induces a similar effective coupling.