|DATE||August 14 (Wed), 2019|
|INSTITUTE||San Francisco State University|
|TITLE||Lecture 3: Jackiw-Teitelboim gravity on two-dimensional nearly de Sitter spacetime|
|ABSTRACT||Jackiw-Teitelboim gravity is a simple toy model of two-dimensional gravity that describes the low-energy gravitational dynamics of many near-extremal black holes in string theory. The field content of the model is a metric and a scalar field called a dilaton, and with negative cosmological constant its basic solutions are anti de Sitter (AdS) spacetimes where the dilaton grows near its asymptotic boundary. These solutions are called “nearly AdS2” spacetimes, and the gravitational dynamics on them reduces to a model of boundary dynamics sometimes called the “Schwarzian theory.” One reason for the recent attention to this model and to the Schwarzian theory more generally is that the same Schwarzian theory arises as the low-energy effective description of the Sachdev-Ye-Kitaev model.
In these talks I will focus on positive cosmological constant, where Jackiw-Teitelboim gravity has "nearly de Sitter” solutions. In this setting Jackiw-Teitelboim gravity gives us a toy model for genuinely quantum cosmology, and in these talks I will describe how one sums over topologies and computes quantum corrections.
Remarkably, the nearly de Sitter model is an analytic continuation of the more standard model in Euclidean signature with negative cosmological constant. Building upon the recent results of Saad, Shenker, and Stanford, we then find significant evidence that nearly de Sitter gravity is in fact dual not to a boundary quantum mechanics or some such, but rather a matrix integral. For the second talk I will discuss this relation in some detail, along with the basics of matrix integrals that one requires.