Classification of Conformal Carroll Algebras

We classify a one-parameter family, ${\mathfrak{c}\mathfrak{o}\mathfrak{n}\mathfrak{f}\mathfrak{c}\mathfrak{a}\mathfrak{r}\mathfrak{r}}_z(d+1)$, of conformal extensions of the Carroll algebra in arbitrary dimension with $z$ being the anisotropic scaling exponent. We further obtain their infinite-dimensional extensions, ${\widetilde{\mathfrak{c}\mathfrak{o}\mathfrak{n}\mathfrak{f}\mathfrak{c}\mathfrak{a}\mathfrak{r}\mathfrak{r}}}_z(d+1)$, and discuss their corresponding finite-dimensional truncated subalgebras when the scaling exponent is integer or half-integer. For all these conformal extensions, we also constrain the 2-point and 3-point correlation functions with electric and/or magnetic features.