Regularization independent analysis of the origin of two loop contributions to N=1 Super Yang–Mills beta function

Abstract

We present a both ultraviolet and infrared regularization independent analysis in a symmetry preserving framework for the N = 1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out whilst the beta function receives contributions of infrared modes.

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

“…For theories with poor symmetry content, MRI manisfests itself as an important ingredient in the calculation of the universal coefficients of the β-function. In recent works we have verified that MRI is also important to preserve the Slavnov Taylor identities for non-abelian gauge theories and supersymmetric gauge theories [13], [16], [17], [27]. A formal proof for these cases is an ongoing work based on diagrammatics and the quantum action principle [28].…”

Guises and disguises of quadratic divergences

“…Within the approach of Implicit Regularization, the original divergent integral is assumed to be implicitly regularized (see [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]). This allows algebraic manipulations in the integrand.…”

“…Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. This construction, which was called Implicit Regularization (IR), can be generalized to arbitrary loop order to define the leading divergence of a Feynman diagram after subtraction of sub-divergences, as dictated by the local version of the BPHZ forest formula, based on the subtraction of local counter-terms [41][42][43][44][45].…”

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

“…The B coefficients involve regularization dependent terms which somewhat explain the controversial results using different frameworks exposed in Table I. Under the light of the ABBJ anomaly example discussed earlier, one can easily verify that STs in (38) are always accompanied by arbitrary momentum routings and thus setting STs to zero amounts to implement MRI and consequently vector gauge invariance, namely…”

“…For instance in [29,[37][38][39] it was shown that constrained IReg (i.e., systematically setting STs to vanish) is also a necessary condition for supersymmetry invariance. Similar results using different theories were obtained for non-Abelian gauge theories [30,31,38]. More recently, IReg was shown to be useful in dealing with γ 5 algebra issues in Feynman amplitudes [44,60].…”