Nilpotent networks and 4D RG flows

Journal article

Starting from a general N= 2 SCFT, we study the network of 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 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 N= 2 SCFT. The arXiv submission also includes the full dataset of theories which can be accessed with a companion Mathematica script.

Authors: Apruzzi, F; Hassler, F; Heckman, J; Rochais, T

• Publication status: Published
• Peer review status: Peer reviewed
• Journal: Journal of High Energy Physics
• Volume: 2019
• Issue: 5
• Article number: 74
• Publication date: 2019-05-14
• Acceptance date: 2019-04-14
• DOI: 10.1007/JHEP05(2019)074
• EISSN: 1029-8479
• ISSN: 1126-6708
• Keywords: FFR