Abstract
Building on [1], 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 the- ories, 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 when the IR Coulomb-branch chiral ring is empty. In the opposite case, there are anomalies that do not match. An intriguing implication of the mismatch is the existence of a second covariantly constant metric on the conformal manifold (other than the Zamolodchikov metric), which imposes previously unknown restrictions on its holonomy group.
Highlights
Conformal field theories (CFTs) in even spacetime dimensions exhibit two classes of conformal anomalies [3]
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
We explore whether type-B Weyl anomalies for Coulomb-branch operators (CBOs) match in different phases of 4D N = 2 SCFTs with a non-trivial N = 2 conformal manifold
Summary
A very useful aspect of chiral anomalies is ’t Hooft anomaly matching. This is the statement that chiral anomalies match across different scales along an RG flow. There is still a type-B Weyl anomaly, but it receives contributions both from massive degrees of freedom (the G(dil) part) and massless degrees of freedom (the G(IR) part) This anomaly manifests itself as a contact term in the appropriate low-momentum limit of the three-point function Tμμ(q)O(k1)O(k2) , which scales as k2n in momentum space with an overall coefficient. In [1] we focussed on N = 2 SCFTs that have non-trivial superconformal manifolds and explored the properties of type-B Weyl anomalies for N = 2 CBOs (as defined in section 1) on the Higgs-branch moduli space. Let us call GCIJF T the type-B anomalies of CBOs OI , OJ at the superconformal vacuum, and GHIJthe corresponding value of these anomalies on the Higgs branch where conformal symmetry is spontaneously broken by default.
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