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.
Highlights
Part of the issue with understanding relevant perturbations of CFTs is that they grow deep in the infrared
Starting from a general N = 2 SCFT, we study the network of N = 1 SCFTs obtained from relevant deformations by nilpotent mass parameters
In this paper we have shown that a great deal of information on the structure of RG flows for 4D SCFTs can be extracted in the special case of nilpotent mass deformations
Summary
We discuss some general features of nilpotent mass deformations of N = 2 SCFTs. Throughout, we assume the existence of a continuous flavor symmetry algebra which may consist of several simple factors: gUV ≡ gflav = g(fl1a)v × . We see that any further deformations of the nilpotent orbit, namely a candidate flow from theory Ti to a theory Ti+1, will involve precisely these directions Provided no such operators decouple as we flow from the UV to the IR, this shows that the directed graph defined by the Hasse diagram is a network of RG flows. As we will shortly explain, for a given su(2) representation, the highest spin states have lowest scaling dimension To study this and related issues in more detail, it is helpful to have an explicit example where the underlying theory is described by a Lagrangian.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
