Nilpotent networks and 4D RG flows

DOI10.1007/JHEP05(2019)074zbMATH Open1416.83110arXiv1808.10439WikidataQ127876287 ScholiaQ127876287MaRDI QIDQ2315711

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Publication date: 25 July 2019

Published in: (Search for Journal in Brave)

Abstract: Starting from a general $mathcalN=2$ SCFT, we study the network of $mathcalN=1$ 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 $mathcalN=2$ 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 $a_{mathrmIR}/c_{mathrmIR}$ for the entire network of flows associated with a given UV $mathcalN=2$ SCFT. The $extttarXiv$ submission also includes the full dataset of theories which can be accessed with a companion $extttMathematica$ script.

Full work available at URL: https://arxiv.org/abs/1808.10439

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