AdS$_{2}$ holography and the SYK model

Abstract

These are lecture notes based on a series of lectures presented at the XIII Modave Summer School in Mathematical physics aimed at PhD students and young postdocs. The goal is to give an introduction to some of the recent developments in understanding holography in two bulk dimensions, and its connection to microscopics of near extremal black holes. The first part reviews the motivation to study, and the problems (and their interpretations) with holography for AdS 2 spaces. The second part is about the Jackiw-Teitelboim theory and nearly-AdS 2 spaces. The third part introduces the Sachdev-Ye-Kitaev model, reviews some of the basic calculations and discusses what features make the model exciting.

Surface charges toolkit for gravity

“…Analogous to the BF formulation of General Relativity in four dimensions, it is possible to have a similar construction for a gravity theory on a line, i.e., lineal gravity. Recently, this topic has active interest due to its use as a 1 + 1 model in the context of the AdS 2 /CF T 1 conjecture [70,71] and also as a low-energy limits model of near-extremal black holes [72]; in both cases this is a toy model with the attractiveness of being simple enough such that many computation are doable even in a quantum regime.…”

Counting superstrata

“…Black-hole microstates with AdS 2 asymptotics are interesting, particularly because of the claim [114,115] that black-hole microstates must have zero angular momentum in four dimensions (J R = 0 in five dimensions) and fit in an AdS 2 region, and also because of the recent surge of interest in the near-AdS 2 /SYK correspondence [116,117] (for a review of the already large literature see e.g. [118]). One cannot have excitation in global AdS 2 [119,120] because a finite excitation makes the dilaton diverge at the end of the space.…”

Space-time in the SYK model

“…For the SYK model the IR and the near-IR limit are solvable, with evaluations [2,6,8] of the invariant Schwarzian action representing the boundary Gravity degrees of freedom possibly related to JT type [81,82] dual theory [83][84][85][86][87] (See also [88][89][90][91][92][93][94][95][96][97]). …”