On the Supersymmetrization of Galileon Theories in Four Dimensions

TL;DR

This paper investigates the supersymmetrization of Galileon theories in four dimensions using amplitude techniques, revealing which Galileon interactions can be supersymmetrized while maintaining their symmetries.

Contribution

It provides the first detailed analysis of supersymmetrizing Galileon theories, identifying compatible symmetries and constructing supersymmetric extensions for specific Galileon orders.

Findings

Quartic Galileon admits a unique supersymmetrization compatible with shift symmetry.

Enhanced special Galileon symmetry is incompatible with supersymmetry.

Supersymmetrization of cubic and quintic Galileons is limited by shift symmetry preservation.

Abstract

We use on-shell amplitude techniques to study the possible $\mathcal{N}=1$ supersymmetrizations of Galileon theories in 3+1 dimensions, both in the limit of decoupling from DBI and without. Our results are that (1) the quartic Galileon has a supersymmetrization compatible with Galileon shift symmetry ($\phi \to \phi +c + b_\mu x^\mu$) for the scalar sector and an ordinary shift symmetry ($\psi \to \psi + \xi$) for the fermion sector, and it is unique at least at 6th order in fields, but possibly not beyond; (2) the enhanced "special Galileon" symmetry is incompatible with supersymmetry; (3) there exists a quintic Galileon with a complex scalar preserving Galileon shift symmetry; (4) one cannot supersymmetrize the cubic and quintic Galileon while preserving the Galileon shift symmetry for the complex scalar; and (5) for the quartic and quintic Galileon, we present evidence for a supersymmetrization in which the real Galileon scalar is partnered with an R-axion to form a complex scalar which only has an ordinary shift symmetry.