Conformal properties of hypermultiplet actions in six dimensions

TL;DR

This paper investigates the conformal properties of hypermultiplet actions in six dimensions, revealing that scale invariance depends on the scalar field dimension and that classical conformal invariance does not extend to the quantum level.

Contribution

It clarifies the conditions under which 6D hypermultiplet actions are scale-invariant and conformally invariant, highlighting the role of scalar field dimensions and quantum effects.

Findings

Scale invariance requires higher derivatives if scalar dimension is 1.

Classical conformal invariance holds if scalar dimension is 2.

Quantum corrections break conformal invariance at scalar dimension 2.

Abstract

We consider scale-invariant interactions of 6D N=1 hypermultiplets with the gauge multiplet. If the canonical dimension of the matter scalar field is assumed to be 1, scale-invariant lagrangians involve higher derivatives in the action. Though scale-invariant, all such lagrangians are not invariant with respect to special conformal transformations and their superpartners. If the scalar canonical dimension is assumed to be 2, conformal invariance holds at the classical, but not at the quantum level.