Abstract
We consider conformal and ’t Hooft anomalies in six-dimensional mathcal{N} = (1, 0) superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and SU(2)R currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non- supersymmetric CFTs in six dimensions have three independent conformal c-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three c-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies. Following earlier work on the conformal a-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.
Highlights
We describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies
Which depends on three real constants C1T,2T,3T that are linearly related to the ci anomalies. (Here Z = (X, Θ) is a superspace variable that is constructed using the three superspace coordinates (xi, θi).) We argue that the conservation equation obeyed by the stresstensor multiplet imposes one linear constraint on the coefficients C1T,2T,3T, which in turn leads to the relation (1.5) among the ci
Adapting the arguments outlined above to this case, we find that the conformal anomaly coefficients associated with the SU(2)R symmetry can be expressed using two linearly independent ci anomaly coefficients (with the third one given by (1.5)), τ1R = c3, τ2R
Summary
We will prove that N = (1, 0) SCFTs only have two independent ci anomalies In such theories, the three ci coefficients are related by a universal, linear relation dictated by supersymmetry,. In every case supersymmetry imposes one additional linear relation on the coefficients of the corresponding non-supersymmetric correlators. It follows that some of the conformal anomalies related to flavor symmetries, which were defined in (1.4), vanish in all N = (1, 0) SCFTs,. The associated conserved current JμR resides in the stress-tensor supermultiplet, and the conformal anomaly coefficients τ1R,2 and ρR it gives rise to need not satisfy the relations (1.7) that hold for flavor currents.
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