Discovering and quantifying nontrivial fixed points in multi-field models

TL;DR

This paper investigates multicritical universality classes in multi-field models using the functional renormalization group and epsilon-expansion, discovering new fixed points and analyzing their stability and implications for asymptotic safety.

Contribution

It introduces a combined approach using functional renormalization group and epsilon-expansion to identify and analyze fixed points in multi-field models with complex symmetry-breaking patterns.

Findings

Discovery of a new fixed point from interactions between different field sectors.

Absence of infrared-stable fixed points for small N_i.

Models exhibit complete RG trajectories connecting nontrivial fixed points.

Abstract

We use the functional renormalization group and the $\epsilon$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed point solutions for the regime of small $N_i$. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points.