Counting RG flows

Abstract

Interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different "topological sectors" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts -from counting RG walls to AdS/CFT correspondence -will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and "topological obstructions" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts "phase transitions" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections with the superconformal index and classifying spaces of global symmetry groups.

Holographic RG flows for four-dimensional $$ \mathcal{N}=2 $$ SCFTs

“…Finally we would like to point out that various interesting conjectures about the structure of RG flows in quantum field theory were presented in [41,42]. Supersymmetric CFTs with holographic duals and the RG flows connecting them provide a natural playing ground to explore these conjectures and we hope that some of our results may be useful in this context.…”

N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories

“…In any case, having more examples will also hopefully lead us to understand which Lagrangian theories will have a chance to flow to an AD theory, or to some other interesting non-Lagrangian SCFTs; this is related to the problem of better understanding the mechanism at work in the N = 1 deformation introduced in [12][13][14], which is still rather mysterious. It will also be interesting to explore these RG flows using the methods developed in [59,60].…”

Properties of the new $$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity

“…In fact, by imposing additional U(1) symmetry, one may further truncate to 10 scalar fields, while preserving all the interesting critical points. At the end such an analysis will elucidate the phase structure of the ABJM SCFT and will provide a rich testing ground for the "µ-theorem" discussed in [60].…”