Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity

Utku Zorba

We present non- and ultra-relativistic Jackiw-Teitelboim (JT) supergravity as metric BF theories based on the extended Newton-Hooke and extended \(\text{AdS}\) Carroll super-algebras 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 \(N=2\) \(\text{AdS}\) super algebra. Subsequently, we introduce the extended \(\text{AdS}_2\) Carroll super algebra, and the associated invariant metric, as a suitable redefinition of the extended Newton-Hooke super algebra. 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 \(\text{(A)dS}\) 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. (https://arxiv.org/abs/2204.09643)

Keywords:
Jackiw-Teitelboim (JT) supergravity, BF theories, Carroll limit, Non-relativistic limit, Supersymmetry, \(\text{AdS}\) Carroll and Newton-Hooke symmetries.

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