Superconformal N=2, D=5 matter with and without actions

TL;DR

This paper explores new matter couplings in five-dimensional N=2 superconformal theories, including cases without Lagrangians, and constructs related superconformal actions and geometries, advancing the understanding of supergravity matter interactions.

Contribution

It introduces novel matter couplings and superconformal Lagrangians in D=5 N=2 theories, including vector-tensor multiplets and non-hyperkähler hypermultiplets, without requiring initial Lagrangian formulations.

Findings

Discovered new vector-tensor multiplet couplings.

Constructed superconformal Lagrangians for generalized matter systems.

Computed Ricci tensor components of hypercomplex manifolds.

Abstract

We investigate N=2, D=5 supersymmetry and matter-coupled supergravity theories in a superconformal context. In a first stage we do not require the existence of a Lagrangian. Under this assumption, we already find at the level of rigid supersymmetry, i.e. before coupling to conformal supergravity, more general matter couplings than have been considered in the literature. For instance, we construct new vector-tensor multiplet couplings, theories with an odd number of tensor multiplets, and hypermultiplets whose scalar manifold geometry is not hyperkaehler. Next, we construct rigid superconformal Lagrangians. This requires some extra ingredients that are not available for all dynamical systems. However, for the generalizations with tensor multiplets mentioned above, we find corresponding new actions and scalar potentials. Finally, we extend the supersymmetry to local superconformal symmetry, making use of the Weyl multiplet. Throughout the paper, we will indicate the various geometrical concepts that arise, and as an application we compute the non-vanishing components of the Ricci tensor of hypercomplex group manifolds. Our results can be used as a starting point to obtain more general matter-couplings to Poincare supergravity.