Ghostbusters in $f(R)$ supergravity

TL;DR

This paper presents a method to eliminate ghost modes in $f(R)$ supergravity by introducing auxiliary gauge fields, and discusses how to stabilize the scalar potential with matter couplings.

Contribution

The paper introduces the ghostbuster mechanism in $f(R)$ supergravity to remove ghost supermultiplets and stabilizes the scalar potential with matter couplings.

Findings

Ghost modes are removed using auxiliary gauge fields.

Instability in the scalar potential can be cured with matter couplings.

The method effectively eliminates higher-derivative ghost terms.

Abstract

$f(R)$ supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains $R^n$ with $n$ greater than two.We remove the ghost in $f(R)$ supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism~\cite{Fujimori:2016udq}. We show that the mechanism removes the ghost supermultiplet but also terms including $R^n$ with $n\geq3$, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.