Clarifying Some Remaining Questions in the Anomaly Puzzle

We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.Comment: 22 pages, no figure. v2: minor changes. v3: sections re-organized. new subsections (IVA, IVB) added. references adde

Short-Term Longitudinal Relationships Between Children's Peer Victimization/Bullying Experiences and Self-Perceptions Evidence for Reciprocity

This study tested transactional models to explain the short-term longitudinal links between self-perceptions and involvement in bullying and victimization among 115 9- to 10-year-old children. Self-perceptions were measured with Harter's Self-Perception Profile for Children (six sub-scales) and bullying/victimization by means of peer nominations. Data were collected at two points, separated by five months, within a school year. Earlier victimization significantly negatively predicted changes in Global self-worth, social acceptance and, for girls only, physical appearance scores, and earlier social acceptance scores significantly negatively predicted changes in victimization, and bullying. Additionally, earlier bullying positively predicted changes in scholastic competence scores, and among girls but not boys there was a near significant tendency for earlier bullying to negatively predict changes in behavioural conduct scores. These findings challenge a common view that victimization, and separately bullying, are responsible for low self-perceptions. Rather, they add to the view that negative peer experiences and maladjusted outcomes are mutually related over time. The theoretical and practical implications of such a view are discussed