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

Abstract

We analyze 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 SUð2Þ. 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.

Supersymmetry anomaly in the superconformal Wess-Zumino model

“…In particular, R-symmetry is anomalous because of the standard triangle diagram, but both Q-and S-supersymmetries are necessarily also anomalous. On the contrary, the Poincaré supersymmetry of the FZ multiplet (which corresponds to a specific field-dependent linear 11 We note that in this respect there is a similarity with an analogous discussion of the supersymmetry anomaly related to gauge/flavor anomalies, where the anomaly is manifest in the WZ gauge [21,22]. There are however also important differences.…”

“…In addition to conformal symmetry and standard supersymmetry (Q-supersymmetry), these theories also have a U(1) R-symmetry and special conformal supersymmetry (S-supersymmetry). It was realised early on that the trace anomaly, the R-current anomaly and S-anomaly sit in a supermultiplet [5] and that one cannot maintain at the same time the conservation of the Q and S supersymmetry [6][7][8][9][10][11]. This is the standard superconformal anomaly mentioned and is distinct from the anomaly discussed here.…”

“…In particular, W ren [e, A, ψ, M ] may be identified with what was termed the 'minimal Q-supersymmetric scheme', while W [e, A, ψ] was referred to as the 'Wess-Zumino scheme' in [22]. 11 However, a more detailed comparison between the two analyses, including the general form of the finite counterterm W fin , is beyond the scope of the present work.…”

Two-loop gauge coupling $β$-function in a four-dimensional framework: the Standard Model case

“…As an effort to circumvent these problems, other regularization methods have been proposed, which aim to stay in the physical dimension as far as possible (see [4,5] for a review). However, as recently pointed out [6], they may also suffer from similar issues in general (see also [7][8][9] for particular examples). Nevertheless, since some of these methods aim to perform regularization/renormalization at integrand level, they may be more effective and prone to a numerical approach.…”

Gauge-covariant diagonalization of $π$-$a_1$ mixing and the resolution of a low energy theorem

“…where b 2 is dimensionless and as yet undetermined. This constitutes a further example in which an arbitrary regularization dependent parameter should be fixed by the physical requirements [26,32,33]. The AAA amplitude would be zero had it been regularized in advance by any regularization that sets ST to zero.…”