Discovering and quantifying nontrivial fixed points in multi-field models

Abstract

We use the functional renormalization group and the $\epsilon$-expansion concertedly to explore multicritical universality classes for coupled ${⨁}_{i}O(N_i)$ 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.

10 pages, 6 figures; minor changes, as published in EPJ C

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Cited by in corpus (8)

• The nonperturbative functional renormalization group and its applications
• Zooming in on fermions and quantum gravity
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Conformal Gauge-Yukawa Theories away From Four Dimensions
• Non-parametric reconstruction of dark energy and cosmic expansion from the Pantheon compilation of type Ia supernovae
• Universal behavior of coupled order parameters below three dimensions
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$