Nilpotent networks and 4D RG flows

Abstract

Abstract Starting from a general $$ \mathcal{N}=2 $$ N = 2 SCFT, we study the network of $$ \mathcal{N}=1 $$ N = 1 SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters are promoted to a chiral superfield, with nilpotent vev. Nilpotent elements of semi-simple algebras admit a partial ordering connected by a corresponding directed graph. We find strong evidence that the resulting fixed points are connected by a similar network of 4D RG flows. To illustrate these general concepts, we also present a full list of nilpotent deformations in the case of explicit $$ \mathcal{N}=2 $$ N = 2 SCFTs, including the case of a single D3-brane probing a D- or E-type F-theory 7-brane, and 6D (G, G) conformal matter compactified on a T 2, as described by a single M5-brane probing a D- or E-type singularity. We also observe a number of numerical coincidences of independent interest, including a collection of theories with rational values for their conformal anomalies, as well as a surprisingly nearly constant value for the ratio a IR /c IR for the entire network of flows associated with a given UV $$ \mathcal{N}=2 $$ N = 2 SCFT. The arXiv submission also includes the full dataset of theories which can be accessed with a companion Mathematica script.