Accidental symmetries and the conformal bootstrap

We study an N=2 supersymmetric generalization of the three-dimensional critical O(N) vector model that is described by N+1 chiral superfields with superpotential W=g₁X∑_iZ_i²+g₂X³. By combining the tools of the conformal bootstrap with results obtained through supersymmetric localization, we argue that this model exhibits a symmetry enhancement at the infrared superconformal fixed point due to g₂ flowing to zero. This example is special in that the existence of an infrared fixed point with g₁,g₂≠0, which does not exhibit symmetry enhancement, does not generally lead to any obvious unitarity violations or other inconsistencies. We do show, however, that the F-theorem excludes the models with g₁,g₂≠0 for N>5. The conformal bootstrap provides a stronger constraint and excludes such models for N>2. We provide evidence that the g₂=0 models, which have the enhanced O(N)×U(1) symmetry, come close to saturating the bootstrap bounds. We extend our analysis to fractional dimensions where we can motivate the nonexistence of the g₁,g₂≠0 models by studying them perturbatively in the 4−ϵ expansion.