All Bulk and Boundary Unitary Cubic Curvature Theories in Three Dimensions

TL;DR

This paper classifies all cubic curvature gravity theories in three dimensions that are unitary both in the bulk and on the boundary, focusing on their relation to known theories like Einstein-Hilbert, NMG, and their extensions.

Contribution

It constructs all parity-invariant cubic curvature gravity theories in 3D that are unitary in bulk and boundary, linking them to known unitary theories and analyzing their extensions.

Findings

Identified all bulk and boundary unitary cubic curvature theories in 3D.

Showed the conflict between unitarity in NMG and boundary unitarity.

Explored unitarity of Born-Infeld extensions of NMG.

Abstract

We construct all the bulk and boundary unitary cubic curvature parity invariant gravity theories in three dimensions in (anti)-de Sitter spaces. For bulk unitarity, our construction is based on the principle that the free theory of the cubic curvature theory reduces to one of the three known unitary theories which are the cosmological Einstein-Hilbert theory, the quadratic theory of the scalar curvature or the new massive gravity (NMG). Bulk and boundary unitarity in NMG is in conflict; therefore, cubic theories that are unitary both in the bulk and on the boundary have free theories that reduce to the other two alternatives. We also study the unitarity of the Born-Infeld extensions of NMG to all orders in curvature.