Superspace evaluation of the two-loop effective potential for the O’Raifeartaigh model

Abstract

All-order spurion-corrected superpropagators and superfield Feynman rules are employed to sys- In the case of supersymmetric theories, the effective potential can be directly calculated in superspace, by using supergraphs. In general, the supereffective action is described by two functions of the chiral and the antichiral superfields; one is required to be a holomorphic function and the other one, called Kähler potential, less constrained, is required to be just a real function. The holomorphic part of the superpontential is very constrained, which is reflected in various nonrenormalization theorems, leading to results to all orders in perturbation theory [1], and even nonperturbative results in some cases [2]. For models with spontaneous supersymmetry (SUSY) breaking, the effective potential can be calculated by using superspace techniques even if soft explicit breaking terms are introduced in the superspace action; this yields spurion insertions. These terms have been carefully classified and studied by Girardello and Grisaru [3]. This approach to study SUSY breaking is very powerful because it leaves most of the supersymmetric structure intact. In fact, as the full supersymmetric and the supersymmetry breaking terms are represented as interactions in superspace, the renormalization can be performed systematically directly in superspace.In general, the background field method is adopted to calculate the effective potential.In this method, the scalar fields of the theory are each separated into a constant classical background plus quantum fluctuations. Using this approach, the effective potential is equal

Supergraph approach in a higher-order linear delta expansion calculation of the effective potential forF-type broken supersymmetry

“…where A, B and C are corrections to the order δ 1 solutions. This naturally brings nonlinear g contributions and generates nonperturbative results that go beyond the one-and two-loop results derived in [13,31].…”

“…This naturally brings nonlinear g contributions and generates nonperturbative results that go beyond the one-and two-loop results derived in Refs. [13,31]. The parameters were chosen so that spontaneous SUSY breaking appears in the O'Raifeartaigh model.…”

“…In order to calculated the two-loop diagrams we are going to use technique developed in [31]. The contribution of the first diagram is given by…”

Observational constraint on interacting Tsallis holographic dark energy in logarithmic Brans–Dicke theory

“…Some observational evidences of the interaction in dark sectors have been found recently [105,106]. Abdalla et al [107,108] have investigated the signature of interaction between DE and dark matter by using optical, X-ray and weak lensing data from the relaxed galaxy clusters. So, it is reasonable to assume the interaction between DE and dark matter in cosmology.…”

Superspace approach to the renormalization of the O’Raifeartaigh model up to the second order in the linear delta expansion parameter

“…We stress that, even though SUSY is broken, a superfield approach is still the most appropriate setup to describe the problem. In a previous contribution [14], it was actually shown, in a systematic way, how all order spurion corrected superpropagators and super-Feynman rules can be employed to compute explicit 1-and 2-loop corrections to effective potentials in a scenario with an F-term breaking of N ¼ 1, D ¼ 4 supersymmetric matter self-coupled model. The main characteristic of the LDE is to use a traditional perturbative approach together with an optimization procedure.…”