The Geometry of SUSY Enhancement

Abstract

We provide a precise geometric picture that demystifies the phenomenon of supersymmetry enhancement along certain RG flows of four-dimensional field theories, recently discovered by Maruyoshi and Song. It applies to theories of arbitrary rank and it is based on a hyperkähler-structure restoration on the moduli space of solutions of (twisted) Hitchin systems, which underly the class-S construction we use as an engineering tool. Along the way, we formulate a necessary algebraic condition for supersymmetry enhancement, and, when enhancement occurs, we are able to derive the Seiberg-Witten geometry and all conformal dimensions of Coulomb-branch operators for the infrared theory, without using a-maximization.

arXiv comment40 pages, 4 figures

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Cited by in corpus (4)

• A slow review of the AGT correspondence
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• No go for a flow
• Aspects of 4d supersymmetric dynamics and geometry