AUTHOR=Lambert N. , Mouland R. , Orchard T. 

TITLE=Non-Lorentzian SU(1, n) Spacetime Symmetry In Various Dimensions

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.864800

DOI=10.3389/fphy.2022.864800

ISSN=2296-424X

ABSTRACT=<p>We discuss non-Lorentzian Lagrangian field theories in 2<italic>n</italic> − 1 dimensions that admit an <italic>SU</italic>(1, <italic>n</italic>) spacetime symmetry which includes a scaling transformation. These can be obtained by a conformal compactification of a 2<italic>n</italic>-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 2<italic>n</italic>-dimensional theory.</p>