Higher derivative quartic vertex of $f(R)$ gravity in light-cone gauge

TL;DR

This paper derives the complete quartic interaction vertex for $R+ ext{alpha} R^2$ gravity in light-cone gauge, exploring its implications for KLT relations and MHV amplitude computations in modified gravity theories.

Contribution

It provides the first explicit derivation of the quartic vertex in $R+ ext{alpha} R^2$ gravity within the light-cone gauge framework.

Findings

Derived the quartic interaction vertex for $R+ ext{alpha} R^2$ gravity.

Discussed the validity of KLT relations in modified gravity.

Analyzed implications for MHV amplitude calculations.

Abstract

In the recent studies of four-dimensional Einstein-Hilbert action, quite a few interesting results such as the Kawai-Lewellen-Tye (KLT) relations, MHV-Lagrangian and quadratic forms have been reported. These results naturally raise an important question: Whether these results are valid for the modified theories of gravity in 4-dimensions? In this work, we consider $R+\alpha\,R^2$ gravity and derive the complete quartic interaction vertex in light-cone gauge. We then discuss the implications of the results for KLT relations, and computing MHV amplitudes.