Completing the Square to Find the Supersymmetric Matter Effective Action Induced by Coupling to Linearized N=1 Supergravity

TL;DR

This paper derives an explicit, supersymmetry-invariant effective action for N=1 supersymmetric matter coupled to linearized supergravity, highlighting the interplay of local and nonlocal terms from auxiliary fields and graviton/gravitino exchange.

Contribution

It provides a complete, explicit quadratic form of the supergravity-induced effective action for matter, including auxiliary, graviton, and gravitino contributions, facilitating studies on supersymmetry breaking.

Findings

Explicit supersymmetry-invariant effective action derived.

Includes local auxiliary field couplings and nonlocal graviton/gravitino exchange terms.

Provides detailed current expressions for Wess-Zumino and supersymmetric Yang-Mills models.

Abstract

We consider generic N=1 supersymmetric matter coupled to linearized N=1 supergravity through the multiplet of currents. By completing the square, we find the effective action giving the leading supergravity induced correction to the matter dynamics, expressed explicitly as a quadratic form in the components of the current multiplet. The effective action is supersymmetry invariant through an interplay of the local terms arising from the auxiliary field couplings, and the nonlocal terms arising from graviton and gravitino exchange, neither of which is separately invariant. Having an explicit form for the supergravity induced effective action is a first step in studying whether supergravity corrections can lead to dynamical supersymmetry breaking in supersymmetric matter dynamics. In Appendices we give explicit expressions for the currents, in our notational conventions, in the Wess-Zumino and supersymmetric Yang Mills models.