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

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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.