Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory

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.

arXiv commentReferences added; complies with published version

References in corpus (43)

• When radiative corrections are finite but undetermined
• Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry
• Facts of life with gamma(5)
• Physical (ir)relevance of ambiguities to Lorentz and CPT violation in QED
• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Anomaly-Free Supersymmetric Models in Six Dimensions
• Towards gauge theories in four dimensions
• Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework
• Techniques for one-loop calculations in constrained differential renormalization
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Four-dimensional unsubtraction from the loop-tree duality
• A four-dimensional approach to quantum field theories
• Using Dimensional Reduction for Hadronic Collisions
• Consistency Relations for an Implicit n-dimensional Regularization Scheme
• Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting ${\gamma }_5$
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
• Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation
• ${\gamma }_5$ in FDH
• Quantum gravitational contributions to the beta function of quantum electrodynamics
• (Un)determined finite regularization dependent quantum corrections: the Higgs decay into two photons and the two photon scattering examples
• Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
• Implicit regularization beyond one loop order: gauge field theories
• Arbitrary parameters in implicit regularization and democracy within perturbative description of 2-dimensional gravitational anomalies
• Momentum routing invariance in Feynman diagrams and quantum symmetry breakings
• An anomalous breaking of supersymmetry in supersymmetric gauge theories with local coupling
• The Infrared Structure of QCD Amplitudes and $H\to gg$ in FDH and DRED
• Arbitrariness in the gravitational Chern-Simons-like term induced radiatively
• Calculating the anomalous supersymmetry breaking in Super-Yang-Mills theories with local coupling
• Gauge Invariant Treatment of ${\gamma }_5$ in the Scheme of 't Hooft and Veltman
• ${\gamma }_5$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$
• Supergravity corrections to the $(g-2{)}_l$ factor by Implicit Regularization
• Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
• Anomalies Dismissed of Ambiguities and the Neutral Pion Decay
• Superconformal Sum Rules and the Spectral Density Flow of the Composite Dilaton (ADD) Multiplet in $\mathcal{N}=1$ Theories
• On the Bose symmetry and the left- and right-chiral anomalies
• Subtleties in the beta function calculation of N=1 supersymmetric gauge theories
• Guises and Disguises of Quadratic Divergences
• Implicit regularization beyond one loop order: scalar field theories
• Maintaining Gauge Symmetry in Renormalizing Chiral Gauge Theories
• Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach
• Note on triangle anomaly with improved momentum cutoff
• Anomaly-Mediated Supersymmetry Breaking Demystified
• Symmetry preserving regularization with a cutoff

Cited by in corpus (4)

• Anomalous Supersymmetry
• Supersymmetry anomalies in new minimal supergravity
• Supersymmetry anomaly in the superconformal Wess-Zumino model
• Higgs boson decay into gluons in a 4D regularization: IR cancellation without evanescent fields to NLO