A note on dualities in Einstein's gravity in the presence of a non-minimally coupled scalar field

TL;DR

This paper demonstrates that Einstein's gravity with a non-minimally coupled scalar field exhibits a conformal invariance leading to dual theories, generalizing known string theory dualities like S-duality.

Contribution

It introduces a new class of conformal dualities in Einstein's gravity with scalar fields, extending the concept of S-duality to more general couplings.

Findings

Identifies a set of conformal transformations leaving the action invariant.

Shows these transformations relate dual theories with scaled effective couplings.

Connects the dualities to known string theory S-duality.

Abstract

We show that the action of Einstein's gravity with a scalar field coupled in a generic way to spacetime curvature is invariant under a particular set of conformal transformations. These transformations relate dual theories for which the effective couplings of the theory are scaled uniformly. In the simplest case, this class of dualities reduce to the S-duality of low-energy effective action of string theory.