A Canticle on (4,0) Supergravity-Scalar Multiplet Systems for a ``Cognoscente''

TL;DR

This paper explores three of four minimal (4,0) scalar multiplets coupled to (4,0) supergravity, highlighting their distinct couplings and the unique conformal coupling of the SM-I multiplet.

Contribution

It identifies the differences in couplings of scalar multiplets to supergravity and clarifies the conditions for conformal invariance in (4,0) supergravity systems.

Findings

Only the SM-I multiplet has a conformal coupling.

Other multiplets require additional curvature or gauge terms.

Distinct couplings are evident at the component level.

Abstract

Extending prior investigations, we study three of the the four distinct minimal (4,0) scalar multiplets coupled to (4,0) supergravity. It is found that the scalar multiplets manifest their differences at the component level by possessing totally different couplings to the supergravity fields. Only the SM-I multiplet possesses a conformal coupling. For the remaining multiplets, terms linear in the world sheet curvature and/or SU(2) gauge field strengths are required to appear in the action by local supersymmetry.