Bootstrapping the O(N) archipelago

We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector ϕ i and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (Δ ϕ , Δ s ) to lie inside small islands. We also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.