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 S4 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.
Highlights
Introduction and summary of resultsIn even spacetime dimensions a conformal field theory (CFT) can exhibit two types of conformal anomalies, type-A and type-B [1]
The main goal of this paper is to examine non-perturbative properties of type-B anomalies for certain integer-dimension operators on the Higgs branch of 4D N = 2 CFTs
We focus on 4D N = 2 superconformal field theories (SCFTs) with non-trivial superconformal manifolds, namely continuous families of N = 2 SCFTs related by exactly-marginal deformations
Summary
In even spacetime dimensions a conformal field theory (CFT) can exhibit two types of conformal anomalies, type-A and type-B [1]. (1) We argue that derivatives of the correlation functions on the Higgs branch with respect to the exactly-marginal couplings can be defined using the same connection on the superconformal manifold that appears in the unbroken CFT phase in the context of conformal perturbation theory. The proposed anomaly matching implies that there is a corresponding set of data for the non-conformal theory on the Higgs branch, which is determined by the same functions of the exactly-marginal couplings. A collection of useful facts as well as our conventions are relegated to a set of appendices at the end of the manuscript
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