Minimal Massive Supergravity.

Minimal massive gravity in three dimensions propagates a single massive spin-2 mode around an anti-de Sitter vacuum. It is distinguished by allowing for vacua with positive central charges of the asymptotic conformal algebra and a bulk graviton of positive energy. We present a new action for the model (and its higher order extensions) in terms of a dreibein and an independent spin connection. From this, we construct its supersymmetric extension. Surprisingly, all vacua complying with bulk and boundary unitarity appear to break supersymmetry spontaneously. In contrast, all supersymmetric vacua have a negative central charge whenever the bulk graviton has positive energy.

Gravity and the Spin-2 Planar Schrödinger Equation.

A Schrödinger equation proposed for the Girvin-MacDonald-Platzman gapped spin-2 mode of fractional quantum Hall states is found from a novel nonrelativistic limit, applicable only in 2+1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3+1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the nonlinear Einstein equations, a confining harmonic oscillator potential for the individual particles.

Three-Dimensional Extended Bargmann Supergravity.

We show that three-dimensional general relativity, augmented with two vector fields, allows for a nonrelativistic limit, different from the standard limit leading to Newtonian gravity, that results in a well-defined action which is of the Chern-Simons type. We show that this three-dimensional "extended Bargmann gravity," after coupling to matter, leads to equations of motion allowing a wider class of background geometries than the ones that one encounters in Newtonian gravity. We give the supersymmetric generalization of these results and point out an important application in the context of calculating partition functions of nonrelativistic field theories using localization techniques.

Spin-3 gravity in three-dimensional flat space.

We present the first example of a nontrivial higher spin theory in three-dimensional flat space. We propose flat-space boundary conditions and prove their consistency for this theory. We find that the asymptotic symmetry algebra is a (centrally extended) higher spin generalization of the Bondi-Metzner-Sachs algebra, which we describe in detail. We also address higher spin analogues of flat space cosmology solutions and possible generalizations.