Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity

TL;DR

This paper develops non- and ultra-relativistic versions of Jackiw-Teitelboim supergravity as BF theories based on extended Newton-Hooke and AdS Carroll superalgebras, expanding on the supersymmetric duality between these algebraic structures.

Contribution

It introduces new non- and ultra-relativistic JT supergravity models using extended superalgebras and demonstrates their derivation from expansions of $ ext{N}=2$ JT supergravity.

Findings

Constructed non-relativistic and ultra-relativistic JT supergravity actions.

Established algebraic dualities between Newton-Hooke and Carroll superalgebras.

Showed these theories can be obtained via algebraic expansions of $ ext{N}=2$ JT supergravity.

Abstract

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 $\mathcal{N}=2$ 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 $\mathcal{N}=2$ JT supergravity.