Supersymmetric Localization and Nonconformal N=2 Supersymmetric Yang-Mills Theories in the Perturbative Regime

Abstract

We examine the relation between supersymmetric localization on S4 and standard QFT results for nonconformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU(N) N=2 supersonic Yang-Mills theories with massless hypermultiplets in an arbitrary representation R such that the β function is nonvanishing. On S4, localization maps this observable into an interacting matrix model. Despite broken conformal symmetry at the quantum level, we show that within a specific regime of validity the matrix model predictions are consistent with perturbation theory in flat space up to order g6. At this order, the reorganization of Feynman diagrams based on the matrix model potential, which has been widely tested in conformal models, also applies in nonconformal setups and is realized, in perturbative field theory, through highly nontrivial interference mechanisms. Published by the American Physical Society 2025