Einstein’s gravitational field equations, which relate the geometry of spacetime to the matter in it, can also be applied to a spacetime of three dimensions (3D) but in this case the matter completely determines the geometry, so there is no “room” for gravitational waves: gravitons in the quantum theory. However, in 3D there is a simple extension of Einstein’s second-order equations to the third-order equations of “Topologically-Massive Gravity” (TMG), which propagates a single massive spin-2 mode; i.e. a massive graviton.
In the context of asymptotically anti-de Sitter (AdS) space times, both 3D Einstein gravity and TMG are potentially semi-classical approximations to some consistent 3D quantum gravity theory defined, via the AdS/CFT correspondence, in terms of a 2D conformal field theory (CFT). However, Continue reading