Superconformal Sigma Models in Higher Than Two Dimensions

TL;DR

This paper constructs superconformal sigma models in dimensions higher than two, utilizing conformal Killing spinors and vectors, and extends previous singleton models to new higher-dimensional settings.

Contribution

It introduces new superconformal sigma models in higher dimensions based on conformal Killing structures, generalizing earlier singleton actions.

Findings

Models exhibit manifest worldvolume conformal symmetry.

Construction of gauged sigma models with conformal supersymmetry.

Extension of singleton actions to higher-dimensional contexts.

Abstract

Rigidly superconformal sigma models in higher than two dimensions are constructed. These models rely on the existence of conformal Killing spinors on the $p+1$ dimensional worldvolume $(p\le 5)$, and homothetic conformal Killing vectors in the $d$--dimensional target space. In the bosonic case, substituting into the action a particular form of the target space metric admitting such Killing vectors, we obtain an action with manifest worldvolume conformal symmetry, which describes the coupling of $d-1$ scalars to a conformally flat metric on the worldvolume. We also construct gauged sigma models with worldvolume conformal supersymmetry. The models considered here are generalizations of the singleton actions on $S^p\times S^1$, constructed sometime ago by Nicolai and these authors.