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

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.

59 pages; v2: typos corrected and references added; v3: a previously incomplete argument regarding the covariant constancy of the anomaly has been confirmed by more recent results, references added and typos corrected; v4: error in the perturbative calculation of the N=2 quiver case amended

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• (Mis-)Matching Type-B Anomalies on the Higgs Branch
• Comments on Quivers and Fractons
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Integrability treatment of AdS/CFT orbifolds
• Covariantly Constant Anomalies on Conformal Manifolds
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• On the trace anomaly of Chaudhuri-Choi-Rabinovici model
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography