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Non-Perturbative Constraints on Light Sparticles from Properties of the RG Flow

We study certain small supersymmetry-breaking perturbations of a large class of strongly coupled four-dimensional R-symmetric renormalization group (RG) flows between superconformal field theories in the ultraviolet (UV) and the infrared (IR). We analyze the conditions under which these perturbations scale to zero at leading order in the deep IR, resulting in accidental supersymmetry. Furthermore, we connect the emergence of IR supersymmetry in this context with a quantity that was recently conjectured to be larger at the UV starting points of the underlying supersymmetric flows than at the corresponding IR endpoints, and we propose a bound on emergent supersymmetry. Along the way, we prove a simple and useful non-perturbative theorem regarding the IR behavior of global flavor currents. Our results suggest general ways in which light stop particles can emerge and potentially influence physics at the Large Hadron Collider.