Type-B Anomaly Matching and the 6D (2,0) Theory

TL;DR

This paper investigates conformal anomalies in 4D N=2 superconformal field theories, showing they are covariantly constant on conformal manifolds and can be computed exactly, with applications to 6D (2,0) theories via 4D localization.

Contribution

It demonstrates that type-B anomalies are covariantly constant on conformal manifolds and establishes their matching in broken and unbroken phases, providing a new computable data set for Higgs branches.

Findings

Anomalies are covariantly constant on conformal manifolds.

Anomaly matching occurs between broken and unbroken phases.

Localization computes non-trivial 6D (2,0) data from 4D theories.

Abstract

We study type-B conformal anomalies associated with $\frac{1}{2}$-BPS Coulomb-branch operators in 4D $\mathcal N=2$ superconformal field theories. When the vacuum preserves the conformal symmetry these anomalies coincide with the two-point function coefficients in the Coulomb-branch chiral ring. They are non-trivial functions of exactly-marginal couplings that can be determined from the $S^4$ partition function. In this paper, we examine the fate of these anomalies in vacua of the Higgs-branch moduli space, where conformal symmetry is spontaneously broken. We argue non-perturbatively that these anomalies are covariantly constant on conformal manifolds. In some cases, this can be used to show that they match in the broken and unbroken phases. Thus, we uncover a new class of data on the Higgs branch of 4D $\mathcal N=2$ conformal field theories that are exactly computable. An interesting application of this matching occurs in $\mathcal N=2$ circular quivers that deconstruct the 6D (2,0) theory on a torus. In that context, we argue that 4D supersymmetric localisation can be used to calculate non-trivial data involving $\frac{1}{2}$-BPS operators of the 6D theory as exact functions of the complex structure of the torus.