Structure of Carrollian (conformal) superalgebra

A bstract In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both d = 4 and d = 3. For the super-Carrollian algebra in d = 4, we identify multiple admissible structures, depending on the representations of the supercharges with respect to the Carrollian rotation. Some of these structures can be derived by taking the speed of light c → 0 limit from super-Poincaré algebra, but others are completely novel. In the conformal case, we derive nontrivial Carrollian superconformal algebras in dimensions d = 4 and d = 3. Among these, the superconformal algebra in d = 4 and one of the algebras in d = 3 exhibit isomorphisms to the super-Poincaré algebras in d = 5 and d = 4, respectively. Additionally, we identify a novel, nontrivial superconformal algebra in d = 3 that is not isomorphic to any super-Poincaré algebra. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Given that BMS 4 algebra constitutes the infinite-dimensional extension of the d = 3 Carrollian conformal algebra, their supersymmetric extension gives rise to nontrivial superconformal Carrollian algebras. Specifically, we demonstrate the existence of a singlet super-BMS 4 algebra emerging from the extension of the d = 3 Carrollian superconformal algebra, as well as a multiplet super-BMS 4 algebra that does not admit this methodology, as its finite-dimensional subalgebra incorporates supercharges with conformal dimension ∆ = ± $$ \frac{3}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> .