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

Abstract

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.

28 pages; v2:clarifications and references added, some minor changes

References in corpus (3)

• Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
• Variant supercurrent multiplets
• Clarifying Some Remaining Questions in the Anomaly Puzzle

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• On the Trace Anomaly and the Anomaly Puzzle in N=1 Pure Yang-Mills
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• Loop Corrected Supercharges from Holomorphic Anomalies