Supersymmetric Galileons

TL;DR

This work develops ${\cal N}=1$ supersymmetric extensions of conformal Galileon theories by starting from ghost condensate physics. It shows how to cure fermion gradient instabilities through carefully constructed SUSY higher-derivative terms, revealing a deep connection between ghost condensates and conformal Galileons. Explicit SUSY extensions are constructed up to ${\cal L}_4$, with a healthy quartic case achieving covariant fluctuations and preserved auxiliary-field structure. The authors also expose subtle stress-energy tensor ambiguities in higher-derivative theories, discuss NEC violation, and outline potential paths toward supergravity embeddings and cosmological applications. Overall, the results establish a viable SUSY Galileon framework that supports stable NEC-violating backgrounds and motivates further exploration of SUSY extensions and gravitational couplings.

Abstract

Galileon theories are of considerable interest since they allow for stable violations of the null energy condition. Since such violations could have occurred during a high-energy regime in the history of our universe, we are motivated to study supersymmetric extensions of these theories. This is carried out in this paper, where we construct generic classes of N=1 supersymmetric Galileon Lagrangians. They are shown to admit non-equivalent stress-energy tensors and, hence, vacua manifesting differing conditions for violating the null energy condition. The temporal and spatial fluctuations of all component fields of the supermultiplet are analyzed and shown to be stable on a large number of such backgrounds. In the process, we uncover a surprising connection between conformal Galileon and ghost condensate theories, allowing for a deeper understanding of both types of theories.