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 T2, 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 aIR/cIR for the entire network of flows associated with a given UV \( \mathcal{N}=2 \) SCFT. The arXiv submission also includes the full dataset of theories which can be accessed with a companion Mathematica script.
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Apruzzi, F., Hassler, F., Heckman, J.J. et al. Nilpotent networks and 4D RG flows. J. High Energ. Phys. 2019, 74 (2019). https://doi.org/10.1007/JHEP05(2019)074
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DOI: https://doi.org/10.1007/JHEP05(2019)074