2D $F(R)$ gravity and AdS$_2$/CFT$_1$ correspondence

TL;DR

This paper explores the canonical structure of 2D $F(R)$ gravity, its equivalence to Jackiw-Teitelboim gravity and Sachdev-Ye--Kitaev models under AdS$_2$/CFT$_1$ correspondence, and examines the singular $D o 2$ limit where this correspondence breaks down.

Contribution

It demonstrates the equivalence of 2D $F(R)$ gravity with Jackiw-Teitelboim gravity and Sachdev-Ye--Kitaev models, and analyzes the breakdown of AdS$_2$/CFT$_1$ correspondence in the singular limit.

Findings

$F(R)$ gravity is equivalent to Jackiw-Teitelboim gravity without matter.

Under AdS$_2$/CFT$_1$, $F(R)$ gravity corresponds to Sachdev-Ye--Kitaev models.

The AdS$_2$/CFT$_1$ correspondence does not hold in the $D o 2$ singular limit.

Abstract

We studied the canonical structure of 2D $F(R)$ gravity. Its equivalence with Jackiw-Teitelboim gravity is demonstrated when no matter presents. Then, due to AdS$_2$/CFT$_1$ correspondence, such $F(R)$ gravity is equivalent to the Sachdev-Ye--Kitaev models. The singular $D\to 2$ limit of $F(R)$ gravity is also studied. It is shown that in such a limit AdS$_2$/CFT$_1$ correspondence is not realized.