Supergravity Tensor Calculus in 5D from 6D

TL;DR

This work constructs a full 5D supergravity tensor calculus by dimensionally reducing the 6D superconformal framework, retaining the dilatation symmetry to ease canonicalization of the Einstein term. It explicitly derives the 5D Weyl multiplet and matter multiplet transformations, including an off-shell hypermultiplet obtained from the 6D on-shell hypermultiplet, and develops invariant action formulas and embedding relations to couple general matter–Yang–Mills systems to supergravity. The paper's embedding structures, notably central-charge vector multiplets and polynomial embeddings of vector and hypermultiplets into linear multiplets, provide a versatile toolkit for building general 5D supergravity theories with varied compensator choices. These results enable systematic construction of 5D matter–gravity systems and lay the groundwork for phenomenological applications and future compensator-based formulations in 5D supergravity.

Abstract

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus still retains the dilatation gauge symmetry so that it becomes a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system.