Born-Infeld extension of new massive gravity

TL;DR

This paper introduces a three-dimensional Born-Infeld gravity theory that extends New Massive Gravity to all orders in curvature, potentially offering a consistent quantum gravity framework.

Contribution

It develops a Born-Infeld extension of NMG that matches known deformations at low orders and extends to all orders, suggesting a new approach to quantum gravity.

Findings

Reduces to NMG at quadratic order in curvature

Reproduces NMG deformation from AdS/CFT at cubic order

Provides a consistent all-order curvature extension

Abstract

We present a three-dimensional gravitational Born-Infeld theory which reduces to the recently found New Massive Gravity (NMG) at the quadratic level in the small curvature expansion and at the cubic order reproduces the deformation of NMG obtained from AdS/CFT. Our action provides a remarkable extension of NMG to all orders in the curvature, and might define a consistent quantum gravity.