${\cal N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions

TL;DR

This paper explores the relations between conformal and 't Hooft anomalies in six-dimensional ${ m N}=(1,0)$ superconformal theories, revealing how supersymmetry constrains anomaly structures and providing exact results for correlators.

Contribution

It introduces anomaly multiplet relations in 6D ${ m N}=(1,0)$ SCFTs, linking conformal anomalies to 't Hooft anomalies, and demonstrates their utility with explicit examples.

Findings

Supersymmetry reduces the number of independent conformal anomalies.

Anomaly multiplet relations express conformal anomalies in terms of 't Hooft anomalies.

Exact results for correlators are obtained in several interacting theories.

Abstract

We consider conformal and 't Hooft anomalies in six-dimensional ${\cal N}=(1,0)$ 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.