Real-time methods in JT/SYK holography

TL;DR

This paper extends holographic methods to real-time scenarios in JT/SYK models, proposing a consistent framework with closed time contours, and explores implications for boundary averaging and the factorization problem.

Contribution

It introduces a novel real-time holographic prescription using closed time contours for JT/SYK duality, addressing boundary averaging and the factorization issue.

Findings

Closed contours are necessary for 2D holographic duals.

The extended formulas accommodate averaging over couplings.

Averaging induces effective couplings that resolve the factorization paradox.

Abstract

We study the conventional holographic recipes and its real-time extensions in the context of the correspondence between SYK quantum mechanics and JT gravity. We first observe that only closed contours are allowed to have a 2d space-time holographic dual. Thus, in any real-time formulation of the duality, the boundaries of a classical connected geometry are a set of closed curves, parameterized by a complex \emph{closed} time contour as in the Schwinger-Keldysh framework. Thereby, a consistent extension of the standard holographic formulas is proposed, in order to describe the correspondence between gravity and boundary quantum models that include averaging on the coupling constants. We investigate our prescription in different AdS$_{1+1}$ 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.