Abstract
We construct $\mathcal{N}=1$ supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of K\"ahler potential and superpotential up to quadratic order. We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom. We also investigate the nonlocal effects on the supersymmetry breaking and find that supertrace (mass) formula is significantly modified even at the tree level.
Highlights
Higher derivative action for chiral superfieldsWe would like to introduce a higher derivative extension of the standard SUSY action for chiral superfields
Based on such backgrounds, we wish to incorporate SUSY in nonlocal field theories
We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom
Summary
We would like to introduce a higher derivative extension of the standard SUSY action for chiral superfields. S = d4xd4θ K(Φi, Φ†i , Dα, Dα ̇ , ∂μ) + d4xd2θ W (Φi, Φ†i , Dα, Dα ̇ , ∂μ) + h.c. Where the Kahler potential K, and the superpotential W , constructed from Φi’s, Φ†i ’s, and their derivatives are vector and chiral superfields, respectively. This makes the action (2.1) SUSY because super transformations of D-terms and F-terms are total derivatives.. In the following we shall construct a higher derivative action of the form (2.1) up to the second order in Φi and Φ†i , and introduce a SUSY nonlocal field theory This makes the action (2.1) SUSY because super transformations of D-terms and F-terms are total derivatives. In the following we shall construct a higher derivative action of the form (2.1) up to the second order in Φi and Φ†i , and introduce a SUSY nonlocal field theory
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