Conformal properties of hypermultiplet actions in six dimensions
E. A. Ivanov, A. V. Smilga
TL;DR
This work investigates conformal properties of six-dimensional ${\cal N}=(1,0)$ gauge theories coupled to hypermultiplets, using harmonic superspace to build scale-invariant higher-derivative actions. The authors show that for a canonical matter dimension ${d=1}$, the constructed HD actions are not conformally invariant under special conformal transformations, with their conformal variation reducible to total harmonic derivatives. They also analyze a noncanonical ${d=2}$ case, which is classically conformal but develops quantum anomalies similar to the pure gauge theory, including a positive beta function and quadratic divergences. Additionally, they explore a spinor analytic multiplet and conclude that these HD constructions either propagate infinite towers of fields or fail to preserve conformal symmetry. Overall, the findings indicate that achieving anomaly-free conformal invariance in these 6D HD hypermultiplet–gauge systems remains elusive within the studied framework.
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.