Multiple Mass Hierarchies from Complex Fixed Point Collisions

TL;DR

The paper explores how pairs of complex fixed points near the real axis can produce multiple, potentially large, mass hierarchies in renormalization group flows, with examples at weak and strong coupling.

Contribution

It demonstrates that multiple hierarchies can arise from complex fixed point collisions and constructs complex flows, including those violating the $c$-theorem.

Findings

Complex fixed points generate multiple mass hierarchies.

Parametric enhancement of hierarchies is possible.

Constructed flows between complex fixed points, including $c$-theorem violations.

Abstract

A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the real axis and to one another generate multiple hierarchies, some of which can be parametrically enhanced. We illustrate this effect at weak coupling with field-theory examples, and at strong coupling using holography. We also construct complex flows between complex fixed points, including flows that violate the $c$-theorem.