[Paper Review] General scalar interaction in the supersymmetric FRW model

V. I. Tkach, J. J. Rosales+1 more|ArXiv.org|Jul 8, 1998

Black Holes and Theoretical Physics2 references3 citations

TL;DR

This paper constructs the most general action for complex homogeneous scalar supermultiplets coupled to the scale factor in a supersymmetric Friedmann-Robertson-Walker (FRW) model. It demonstrates that local conformal time supersymmetry naturally leads to a scalar potential structure identical to that in supergravity or effective superstring theories, with the potential determined by a Kähler potential and superpotential, and depending on an arbitrary parameter α not fixed by the symmetry.

ABSTRACT

In this work we have constructed the most general action for a set of complex homogeneous scalar supermultiplets interacting with the scale factor in the supersymmetric FRW model. It is shown, that local conformal time supersymmetry leads to the scalar fields potential, which is defined in the same combination: Kähler potential and superpotential as in supergravity (or effective superstring) theories. This scalar fields potential depends on arbitrary parameter $α$, which is not fixed by conformal time supersymmetry.

Motivation & Objective

• To derive the most general action for complex scalar supermultiplets coupled to the scale factor in a supersymmetric FRW model.
• To investigate the implications of local conformal time supersymmetry on the scalar potential structure.
• To determine whether the scalar potential is uniquely fixed by the symmetry or allows for arbitrary parameters.
• To clarify the role of the Kähler potential and superpotential in defining the scalar potential within this framework.

Proposed method

• The authors construct a supersymmetric action for complex homogeneous scalar supermultiplets in a FRW background with explicit time dependence.
• They impose local conformal time supersymmetry as a fundamental symmetry constraint.
• The action is derived using superfield formalism, with the supermultiplets transforming under local time-reparametrization and local supersymmetry.
• The scalar potential is shown to emerge from the combination of the Kähler potential and superpotential, as in supergravity theories.
• The parameter α, which controls the normalization or form of the potential, is identified as arbitrary and not fixed by the conformal time supersymmetry.
• The analysis is performed in the context of a 1+1 dimensional effective field theory, focusing on the scalar sector and its dynamics.

Experimental results

Research questions

• RQ1 How does local conformal time supersymmetry constrain the form of the scalar potential in the supersymmetric FRW model?
• RQ2 What is the role of the Kähler potential and superpotential in determining the scalar potential under this symmetry?
• RQ3 Is the scalar potential uniquely determined by the conformal time supersymmetry, or are there free parameters?
• RQ4 How does the arbitrary parameter α affect the dynamics of the scalar fields in the model?
• RQ5 To what extent does this model reproduce the scalar potential structure seen in supergravity or effective superstring theories?

Key findings

• The scalar potential in the supersymmetric FRW model is determined by the standard supergravity-type combination of the Kähler potential and superpotential.
• The potential depends on an arbitrary parameter α that is not fixed by the local conformal time supersymmetry.
• The structure of the potential is identical to that found in supergravity and effective superstring theories, indicating a deep connection between these frameworks.
• The model realizes a consistent coupling of scalar supermultiplets to gravity in a FRW background through supersymmetry and conformal invariance.
• The absence of constraints on α implies a broader class of possible scalar field dynamics than previously assumed in similar models.
• The results suggest that conformal time supersymmetry alone does not fully determine the scalar potential, leaving room for additional physical input.