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 Nc(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 Nc(d) for 3 ≤ d < 4. Our results show that Nc> 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.