Supersymmetric P(X,phi) and the Ghost Condensate

TL;DR

This paper develops a constructive method to embed higher-derivative scalar theories of the form $P(X,\phi)$ into four-dimensional ${\cal N}=1$ supersymmetry by promoting a power-series expansion in $X$ to superspace building blocks. It applies the framework to produce supersymmetric DBI actions with arbitrary warp factors and to formulate the supersymmetric ghost condensate, carefully analyzing perturbations around time-dependent backgrounds and the interplay with NEC violation. The analysis reveals that supersymmetry introduces additional fields whose fluctuations can be stabilized with appropriately chosen higher-derivative terms, although some fermionic gradient instabilities persist within the basic construction, motivating extensions such as SUSY Galileons and coupling to supergravity. The work provides a practical, general framework for incorporating higher-derivative scalars in ${\cal N}=1$ SUSY and highlights implications for early-universe cosmology and string-inspired effective theories.

Abstract

We show how to construct supersymmetric actions for higher-derivative scalar field theories of the form P(X,phi), within the context of d=4, N=1 supersymmetry. This construction is of general use, and is applied to write supersymmetric versions of the Dirac-Born-Infeld action. Our principal application of this formalism is to construct the supersymmetric extension of the ghost condensate. This allows us to study the interplay between supersymmetry, time-dependent backgrounds and violations of the null energy condition.