Carrollian and non-relativistic Jackiw–Teitelboim supergravity

We present non- and ultra-relativistic Jackiw–Teitelboim (JT) supergravity as metric BF theories based on the extended Newton–Hooke and extended AdS Carroll superalgebras in two spacetime dimensions, respectively. The extended Newton–Hooke structure, and, in particular, the invariant metric necessary for the BF construction of non-relativistic JT supergravity, is obtained by performing an expansion of the $N=2$ AdS ${}_{2}$ superalgebra. Subsequently, we introduce the extended AdS ${}_{2}$ Carroll superalgebra, and the associated invariant metric, as a suitable redefinition of the extended Newton–Hooke superalgebra. The mapping involved can be seen as the supersymmetric extension of the duality existing at the purely bosonic level between the extended Newton–Hooke algebra with (positive) negative cosmological constant and the extended (A)dS Carroll algebra in two dimensions. Finally, we provide the Carrollian JT supergravity action in the BF formalism. Moreover, we show that both the non-relativistic and the ultra-relativistic theories presented can also be obtained by direct expansion of $N=2$ JT supergravity.