Notes on Operator Equations of Supercurrent Multiplets and the Anomaly Puzzle in Supersymmetric Field Theories

Recently, Komargodski and Seiberg have proposed a new type of supercurrent multiplet which contains the energy-momentum tensor and the supersymmetry current consistently. In this paper we study quantum properties of the supercurrent in renormalizable field theories. We point out that the new supercurrent gives a quite simple resolution to the classic problem, called the anomaly puzzle, that the Adler-Bardeen theorem applied to an R-symmetry current is inconsistent with all order corrections to $\beta$ functions. We propose an operator equation for the supercurrent in all orders of perturbation theory, and then perform several consistency checks of the equation. The operator equation we propose is consisitent with the one proposed by Shifman and Vainshtein, if we take some care in interpreting the meaning of non-conserved currents.Comment: 28 pages; v2:clarifications and references added, some minor change

Non-uniform spacings processes

Spacings, Empirical process, Order statistics, Invariance principles, Quantile process, Gaussian process, Brownian bridge,