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

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.