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

TL;DR

This paper investigates type-B conformal anomalies in 4D N=2 SCFTs on the Higgs branch, demonstrating anomaly matching and exploring implications for the conformal manifold's geometry and holonomy.

Contribution

It provides the first non-perturbative verification of anomaly matching for Coulomb-branch anomalies and links potential anomaly mismatches to geometric constraints on the conformal manifold.

Findings

Type-B anomalies match on the Higgs branch in Lagrangian theories.

Non-perturbative anomaly calculations involve multi-loop banana integrals.

Potential anomaly mismatch suggests additional covariantly constant metric on the conformal manifold.

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.