Nilpotent Networks and 4D RG Flows

Abstract

Starting from a general $\mathcal{N}=2$ SCFT, we study the network of $\mathcal{N}=1$ 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 $\mathcal{N}=2$ 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 $a_{\mathrm{IR}}/c_{\mathrm{IR}}$ for the entire network of flows associated with a given UV $\mathcal{N}=2$ SCFT. The $\text{arXiv}$ submission also includes the full dataset of theories which can be accessed with a companion $\text{Mathematica}$ script.

arXiv commentv2: 73 pages, 12 figures, clarifications and references added

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• Geometric Unification of Higgs Bundle Vacua
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