Bootstrapping frustrated magnets: The fate of the chiral O(N) × O(2) universality class

We study multiscalar theories with O(N) × 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 ≼ 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.