Born-Infeld extension of new massive gravity

TL;DR

The paper constructs a three-dimensional gravitational Born-Infeld theory that reproduces New Massive Gravity (NMG) at quadratic order in curvature and, at cubic order, matches the AdS/CFT deformation of NMG constrained by a holographic c-theorem. The action is a determinantal Born-Infeld extension built from the cosmological Einstein tensor $\mathcal{G}_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R-m^{2}g_{\mu\nu}$, with a cosmological term leading to the CNMG generalization via expansion of $\sqrt{-\det(-\frac{1}{m^{2}}\mathcal{G})}$; the minimal form is $I_{\text{BI}}=-\frac{4m^{2}}{\kappa^{2}}\int d^{3}x\,\left[\sqrt{-\det\left(-\frac{1}{m^{2}}\mathcal{G}\right)}-\sqrt{-\det g}\right]$, and the cosmological extension is $I_{\text{CBI}}=-\frac{4m^{2}}{\kappa^{2}}\int d^{3}x\,\left[\sqrt{-\det\left(-\frac{1}{m^{2}}\mathcal{G}\right)}-\left(\frac{\Lambda}{2m^{2}}+1\right)\sqrt{-\det g}\right]$. At $O(R^{3})$ the action generates cubic curvature terms $\frac{2}{3m^{4}}\left(R^{\mu\nu}R_{\nu}^{\ \alpha}R_{\alpha\mu}-\frac{9}{8}R R_{\mu\nu}^{2}+\frac{17}{64}R^{3}\right)$, reproducing the Sinha AdS/CFT deformation. The framework thus provides a candidate all-orders extension of CNMG with potential UV improvements and connections to string/D-brane physics, with future work including linearization on (A)dS backgrounds, classical solutions, and matter couplings.

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.