Potencial efetivo em teorias supersimétricas com altas derivadas

Abstract

Higher derivative theories were introduced quite early in an attempt to regularize the ultraviolet divergencies of quantum field theories. Unfortunately, higher derivatives theories have an energy which is not bounded from below and seem to lead to ghosts, states with negative norm, that violate the unitarity. In spite of that, higher derivative theories have better renormalisation properties than the conventional theories and thus have been thoroughly studied. Recently, in the context of supersymmetric theories the interest in this subject has been stimulated by the studies about, for instance, the higher derivative regularization method, the higher derivative supergravity model, the classical aspects of the higher derivative chiral superfield models, and so on. In 2009, Gomes, Nascimento, Petrov and da Silva calculated the effective superpotential for two versions of higher derivative chiral superfield models. So far no calculation was performed to determine the effective superpotential for some kind of version of higher derivative supersymmetric gauge theory. We fill out this gap with the construction of a consistent higher derivative supersymmetric gauge theory coupled to a chiral matter and with the calculation of the Kälerian contributions to the one-loop effective superpotential. We use the standard Feynman supergraphs techniques in order to obtain such contributions. In the present study, we show that the one-loop Kählerian effective superpotential to the higher derivative supersymmetric abelian gauge theory does not display any divergences, unlike the usual gauge theories.