Non-Lorentzian $SU(1,n)$ Spacetime Symmetry in Various Dimensions

TL;DR

This paper explores non-Lorentzian field theories in odd dimensions with $SU(1,n)$ symmetry, derived from conformal compactification of higher-dimensional Minkowski theories, analyzing their algebra, representations, and examples.

Contribution

It introduces a class of non-Lorentzian theories with $SU(1,n)$ symmetry, detailing their algebraic structure, representations, and methods to reconstruct parent theories from lower-dimensional models.

Findings

Identified $SU(1,n)$ as a spacetime symmetry in non-Lorentzian theories.

Provided explicit examples of free theories in various dimensions.

Outlined the reconstruction process of higher-dimensional parent theories.

Abstract

We discuss non-Lorentzian Lagrangian field theories in $2n-1$ dimensions that admit an $SU(1,n)$ spacetime symmetry which includes a scaling transformation. These can be obtained by a conformal compactification of a $2n$-dimensional Minkowskian conformal field theory. We discuss the symmetry algebra, its representations including primary fields and unitarity bounds. We also give various examples of free theories in a variety of dimensions and a discussion of how to reconstruct the parent $2n$-dimensional theory.