Classification of Conformal Carroll Algebras

TL;DR

This paper classifies a family of conformal extensions of the Carroll algebra, explores their infinite-dimensional counterparts, and analyzes the constraints on their correlation functions across various dimensions and scaling exponents.

Contribution

It introduces a new classification of conformal Carroll algebras and their extensions, including infinite-dimensional structures and correlation function constraints.

Findings

Classification of conformal Carroll algebras for arbitrary dimension and scaling exponent.

Derivation of infinite-dimensional extensions of these algebras.

Constraints on 2-point and 3-point correlation functions with electric/magnetic features.

Abstract

We classify a one-parameter family, $\mathfrak{confcarr}_z(d+1)$, of conformal extensions of the Carroll algebra in arbitrary dimension with $z$ being the anisotropic scaling exponent. We further obtain their infinite-dimensional extensions, $\widetilde{\mathfrak{confcarr}}_z(d+1)$, 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.