Applied foliated conformal Carroll symmetries

A bstract We apply the conformal compensating technique for constructing matter couplings to conformal scalars on a D -dimensional foliated conformal Carroll manifold dividing the tangent space into ( p + 1)-dimensional longitudinal and ( D − p − 1)-dimensional transversal directions corresponding to p -branes. We show that the conformal Carroll algebra that was used for particle-like foliated geometries with p = 0 cannot be used for higher-dimensional objects, called p -branes, with 0 < p ≤ D − 2. Furthermore, string-like foliated geometries are not suitable for the conformal compensating technique due to the conformal invariance in the longitudinal directions that is present for p = 1. All other cases can be dealt with provided one uses a different conformal extension of the Carroll algebra that amounts to a conformal extension in the longitudinal directions only supplemented with an additional an-isotropic dilatation. By brane-duality similar results hold for foliated Galilean geometries which we present as well. Our results nicely fit in with recent work on foliated Aristotelian geometries.