A conjectured bound on accidental symmetries

In this note, we study a large class of four-dimensional R-symmetric theories, and we describe a new quantity tau(U) which is well defined in these theories. Furthermore, we conjecture that this quantity is larger in the ultraviolet (UV) than in the infrared (IR), i.e., that tau(UV)(U) > tau(IR)(U). While we do not prove this inequality in full generality, it is straightforward to show that our conjecture holds in the subset of theories that do not have accidental symmetries. In addition, we subject our inequality to an array of nontrivial tests in theories with accidental symmetries and dramatically different dynamics both in N = 1 and N = 2 supersymmetry and find that our inequality is obeyed. One interesting consequence of this conjecture is that the mixing of accidental symmetries with the IR superconformal R current is bounded by the UV quantity, tau(UV)(U). To demonstrate the potential utility of this bound, we apply it to the somewhat mysterious SU(2) gauge theory of Intriligator, Seiberg, and Shenker and show that our conjecture, if correct, implies that this theory flows in the IR to an interacting superconformal field theory.