Polyakov-like approach to the modified gravity and other geometric theories

TL;DR

This paper explores a method to reformulate certain modified gravity theories as Einstein-Hilbert actions with extra matter, linking it to string theory techniques and leading to polynomial brane actions.

Contribution

It introduces a novel procedure to rewrite modified gravity actions as Einstein-Hilbert actions with matter, connecting it to Polyakov's string theory approach and polynomial brane actions.

Findings

Reformulation of mimetic gravity and Regge-Teitelboim theories as Einstein-Hilbert actions with matter

Establishment of a connection between this reformulation and Polyakov's string theory trick

Development of a polynomial brane action from the procedure

Abstract

We study the procedure that allows to rewrite the actions of some modified gravity theories like mimetic gravity and Regge-Teitelboim embedding theory as Einstein-Hilbert actions with additional matter contributions. It turns out that this procedure can be applied to brane action, which lead to a polynomial brane action. We also examine the connection between this procedure and Polyakov trick in string theory.