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 phi(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 (Delta(phi), Delta(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.