Ghostbusters in $f(R)$ supergravity

Understand

$f(R)$ 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.