Description
We consider the simplest class of 3d gauge theories, which is N complex scalar fields coupled to an Abelian gauge field. For large N this theory is known to flow to a CFT with SU(N)xU(1) symmetry, but for finite N there is controversy in the literature. The N=2 case is particularly famous, as its believed to describe the Neel-VBS phase transition, which might be experimentally realizable. Previous lattice studies suggested the SU(2)xU(1) symmetry is enhanced to SO(5), but the assumption of no relevant SO(5) singlet was ruled out by the bootstrap. We perform a bootstrap study assuming SO(5) symmetry, and find a point on the boundary of the allowed region that matches large N predictions, and was recently confirmed by a newer lattice study. We also perform a bootstrap study of the N=3 theory, and find a point on the boundary of the allowed region that matches large N, large charge, and lattice predictions.
