On Ghost-free Supersymmetric Galileons

TL;DR

The paper addresses the challenge of constructing ghost-free supersymmetric Galileons by embedding Galilean invariance into superspace. It shows that a quartic supersymmetric Galileon can be realized as the decoupling limit of non-minimally derivative coupled ${\cal N}=1$ new-minimal supergravity (FGKS), yielding a superspace Lagrangian that preserves a super-Galilean shift ${\Phi \rightarrow \Phi + c + b_\mu y^\mu}$ and reproduces the complex Galileon in flat space. The leading component action comprises a Wess-Zumino term, a scalar quartic Galileon piece, and fermion-scalar interactions, with no extra ghost degrees of freedom below the cutoff $\Lambda$. The work also clarifies the role of R-charge in the new-minimal setting, noting that cubic and quintic SUSY Galileons are not obtained within this framework, thereby providing a consistent covariant SUSY extension of the Galileon paradigm.

Abstract

We present consistent supersymmetric theories invariant under the generalization of the Galilean shift symmetry to ${\cal{N}}=1$ superspace. These theories are constructed via the decoupling limit of certain non-minimally derivative coupled supergravities, thus they correspond to the supersymmetrization of the so-called covariant Galileon. Specifically, these theories are constructed in the linearized ${\cal{N}}=1$ new-minimal supergravity set-up where the chiral supermultiplet is minimally coupled to gravity via the standard R-current contact term, and, at the same time, non-minimally derivatively coupled to the Einstein superfield.