Born-Infeld extension of new massive gravity

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.