Geometry of Higgs-branch superconformal primary bundles

Niarchos, Vasilis

Abstract

It is known that the two- and three-point functions of Higgs-branch superconformal primaries in 4d N = 2 superconformal field theories obey nonrenormalization 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 two-dimensional chiral algebras and the sector of Schur operators in four-dimensional N = 2 theories. We also discuss the general interplay between nonrenormalization 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 four-dimensional N = 4 SYM theory that does not require the use of the four-dimensional t t ∗ equations.

Citation

Niarchos, V. (2018). Geometry of Higgs-branch superconformal primary bundles. Physical Review D, 98(6), Article 065012. https://doi.org/10.1103/physrevd.98.065012

• Journal Article Type: Article
• Acceptance Date: Sep 13, 2018
• Online Publication Date: Sep 25, 2018
• Publication Date: Sep 25, 2018
• Deposit Date: Sep 28, 2018
• Publicly Available Date: Sep 28, 2018
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 98
• Issue: 6
• Article Number: 065012
• DOI: https://doi.org/10.1103/physrevd.98.065012
• Public URL: https://durham-repository.worktribe.com/output/1313268
• Related Public URLs: https://arxiv.org/pdf/1807.04296.pdf