Infrared anomaly induced by spontaneous breakdown of supersymmetry

The abelian anti-ghost equation for the standard model in the 't Hooft background gauge

“…of the AAE are the IR anomalies 6 . The corresponding counterterms might cause IR divergences in the next order of perturbative expansion (some examples can be found in the papers by Bandelloni et al [21] and by Clark et al [22] and [23]). A carefully analysis on this point will be presented in the appendix B.…”

A Decoupling Theorem for the BPHZL-Scheme

“…Under certain conditions, it is possible to violate the lower bound r k 3 mentioned by Lowenstein [13]: e.g. a spinorial insertion may have r k =5Â2 [21,22]. The UV-and IR-subtraction-degrees for a 1 PI-(sub)diagram * are given by…”

A possible constructive approach to (super-φ3)4 (III). On the normalization of Schwinger functions

“…e Ixl, one readily obtains the estimates The above treatment still suffers from several limitations and shortcomings, the most conspicuous one of which is that I had to rely on two conjectures in order to reach the final result which critically depends on the existence of the infinite-volume limit of UV-cutoff Schwinger functions and the cluster-property. Tire reader will have noticed the importance of this property for supersymmetry: without clustering, there are long-range interactions, the surface terms cannot be dropped and some kind of anomalous behavior is to be reckoned with, see also [ 15].…”