Geometry of Higgs-branch superconformal primary bundles

Abstract

It is known that the two- and three-point functions of Higgs-branch superconformal primaries in 4d N=2 superconformal field theories obey non-renormalization theorems on N=2 superconformal manifolds. In this paper we prove a stronger statement, that the bundles of Higgs-branch superconformal primaries over N=2 superconformal manifolds are endowed with a flat connection, or equivalently that Higgs-branch superconformal primaries have vanishing Berry phases under N=2 exactly marginal deformations. This statement fits well with the proposed correspondence between the rigid structures of 2d chiral algebras and the sector of Schur operators in 4d N=2 theories. We also discuss the general interplay between non-renormalization theorems and the curvature of bundles of protected operators and provide a new simpler proof of the vanishing curvature of 1/2-BPS operators in 4d N=4 SYM theory that does not require the use of the 4d tt* equations.

36 pages

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• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• On the Kähler-Hodge structure of superconformal manifolds
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Global aspects of moduli spaces of 2d SCFTs