(Mis-)Matching Type-B Anomalies on the Higgs Branch

Abstract

Building on arXiv:1911.05827, we uncover new properties of type-B conformal anomalies for Coulomb-branch operators in continuous families of 4D $\mathcal{N}=2$ SCFTs. We study a large class of such anomalies on the Higgs branch, where conformal symmetry is spontaneously broken, and compare them with their counterpart in the CFT phase. In Lagrangian theories, the non-perturbative matching of the anomalies can be determined with a weak coupling Feynman diagram computation involving massive multi-loop banana integrals. We extract the part corresponding to the anomalies of interest. Our calculations support the general conjecture that the Coulomb-branch type-B conformal anomalies always match on the Higgs branch. On the other hand, we argue that the potential mismatch of anomalies implies the existence of a second covariantly constant metric on the conformal manifold (other than the Zamolodchikov metric), which would impose restrictions on its holonomy group.

46 pages and supplementary Mathematica notebook; v2: references added; v3: typos corrected and comments added; v4: minor corrections and references added; v5: error in the perturbative calculation of the N=2 quiver case amended and conjectures modified to be consistent with recent developments

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Cited by in corpus (9)

• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Integrability treatment of AdS/CFT orbifolds
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Covariantly Constant Anomalies on Conformal Manifolds
• 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