arXiv subjects
Publications and source records attributed to K. Konishi.
We re-examine perturbative and nonperturbative aspects of the beta function in N=1 and N=2 supersymmetric gauge theories, make comments on the recent literature on the subject and discuss the exactness of several known results such as the NSVZ beta function.
By using the standard perturbation theory we study the mass as well as $θ$ parameter dependence of the Seiberg-Witten theory with $SU(2)$ gauge group, supplemented with a $N=1$ supersymmetric as well as a smaller nonsupersymmetric (e.g.) gaugino mass. Confinement persists at all values of the bare vacuum parameter $θ_{ph}$; as it is varied there is however a phase transition at $θ_{ph} =-π, π, 3π, \ldots$. At these values of $θ_{ph}$ the vacuum is doubly degenerate and CP invariance is spontaneously broken à la Dashen. Due to the instanton-induced renormalization effect the low energy effective $θ$ parameter remains small irrespectively of $θ_{ph}$ as long as the gaugino mass is sufficiently small.
We report the "state of the art" of the problem of $B+L$ violation in high-energy electroweak scatterings. Results of various analyses point toward (though do not prove rigorously yet) the "half-suppression", i.e., that the $B+L$ violating cross section remains suppressed at least by the negative exponent of the single instanton action, at all energies. Most interesting techniques developed in this field are reviewed. Particular attention is paid to unitarity constraints on the anomalous cross section, and to some conceptual problem involving the use of the optical theorem in the presence of instantons.
We study the level crossing of the fermion system described by the euclidean Dirac Hamiltonian in the valley background. One chiral fermion level is shown to cross twice the zero value in the case of well-separated instanton-anti-instanton background. Below a critical separation, however, level crossings are absent. The phenomenon can be interpreted as the transition to a gauge field configuration of purely perturbative nature, below a critical instanton-anti-instanton separation. In the context of high-energy electroweak interactions, our findings seem to definitely invalidate some optimistic argument concerning the observability of baryon number violation based on the use of the optical theorem in conjunction with the valley fields.
Problems related to fermions, unitarity and chiral anomaly in high energy electroweak interactions, are investigated. Particular attention is paid to the correct functional integration over fermion fields in the background of instanton-anti\-instanton type configurations. This leads to an expansion of correlation functions in terms of a small parameter, $ρ/R$, when the instanton-antiinstanton separation ($R$) is large compared to their sizes ($ρ$). Applying such a method to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there are no theoretical basis for expecting anomalous cross sections to become observable at energies in the $10$ TeV region.