Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class

TL;DR

This paper uses numerical conformal bootstrap techniques to determine the critical number of components for stable fixed points in $ ext{O}(N) imes ext{O}(2)$ symmetric models, suggesting that models with N=2,3 in three dimensions likely undergo first-order transitions.

Contribution

The study provides rigorous bounds on the critical N for stability in $ ext{O}(N) imes ext{O}(2)$ models using conformal bootstrap, clarifying the nature of phase transitions in these systems.

Findings

$N_c > 3.78$ for $d=3$, indicating no stable fixed point for $N=2,3$

Supports the scenario of first-order transitions in physically relevant models

Demonstrates the effectiveness of conformal bootstrap in constraining conformal windows

Abstract

We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 \leq d < 4$. Our results show that $N_c> 3.78$ for $d = 3$. This favors the scenario that the physically relevant models with $N = 2,3$ in $d=3$ do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms.