Accidental symmetries and the conformal bootstrap

Abstract

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 = g(1) X Sigma(i) Z(i)(2) + g(2)X(3). 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 g(2) flowing to zero. This example is special in that the existence of an infrared fixed point with g(1), g(2) not equal 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 g(1), g(2) not equal 0 for N > 5. The conformal bootstrap provides a stronger constraint and excludes such models for N > 2. We provide evidence that the g(2) = 0 models, which have the enhanced O(N) x 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 g(1), g(2) not equal 0 models by studying them perturbatively in the 4- epsilon expansion.