Abstract
We analyse Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet interacting with a massless Majorana spin-$1/2$ field in the adjoint representation of $SU(2)$. We shed light on a long-standing controversy regarding the perturbative evaluation of the supercurrent anomaly in connection with gauge and superconformal symmetry in different frameworks. We find that only superconformal symmetry is unambiguously broken using an invariant four dimensional regularization and compare with the triangle AVV anomaly. Subtleties related to momentum routing invariance in the loops of diagrams and Clifford algebra evaluation inside divergent integrals are also discussed in connection with finite and undetermined quantities in Feynman amplitudes.
Highlights
Anomaly-mediated symmetry breaking is an important mechanism in field and string theory [1]
Subtleties related to momentum routing invariance in the loops of diagrams and Clifford algebra evaluation inside divergent integrals are discussed in connection with finite and undetermined quantities in Feynman amplitudes
It is well known that in dimensional specific models which includes chiral, supersymmetric and topological field theories, Feynman diagram calculations cannot be handled in standard dimensional regularization
Summary
Anomaly-mediated symmetry breaking is an important mechanism in field and string theory [1]. If a model is known beforehand to be anomaly free, the question of whether there exists or not an invariant scheme is irrelevant, should the imposition of Ward identities order by order in perturbation theory not to be considered a nuisance In this case either, one employs an invariant scheme and performs renormalization using invariant counterterms or uses noninvariant counterterms to compensate the symmetry breaking. The purpose of this work is to shed light on the apparent clash in the perturbative calculation of the quantum symmetry breaking of the supercurrent conservation in N 1⁄4 1 super Yang Mills theory in connection with gauge invariance and the Rarita-Schwinger constraint (the latter known as superconformal, spin-3=2 or supercurrent trace constraint) [53].
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