Speaker
Description
I will show how the existence of an outer automorphism (Out) provides a sufficient condition for the existence of an RG fixed hyperplane (fixed point, separatrix) in the renormalization group (RG) flow of a Quantum Field Theory (QFT). This gives a systematic way to derive non-perturbative all-order constraints on the RG beta functions and provides the mathematical underpinning of 't Hooft's technical naturalness argument. The beta function constraints and associated RG fixed hyperplanes can be computed non-perturbatively without resorting to perturbation theory. Besides well known exact symmetries, I will also discuss the recently discovered so-called goofy transformations. Even though goofy transformations are, by definition, explicitly broken by kinetic terms, they can give rise to all-order stable RG fixed points. I will use the Out constraints to explain why this is the case. Since goofy transformations can control bare scalar mass parameters and scalar portal couplings, they provide a new class of solutions to the electroweak scale hierarchy problem.
| Affiliation | CFTP, IST, University of Lisbon |
|---|---|
| Link to paper | 2603.12318, 2508.02646, 2505.00099 |
| Career status | Postdoc |