Alasdair J. Routh

On the Hamiltonian form of 3D massive gravity

We present a Chern-Simons-like action for the general massive gravity model propagating two spin-2 modes with independent masses in three spacetime dimensions (3D), and we use it to find a simple Hamiltonian form of this model. The number of local degrees of freedom, determined by the dimension of the physical phase space, agrees with a linearized analysis except in some limits, in particular that yielding topologically new massive gravity, which therefore suffers from a linearization instability.

Matter coupling in 3D 'minimal massive gravity

The “Minimal Massive Gravity” (MMG) model of massive gravity in three spacetime dimensions (which has the same anti-de Sitter (AdS) bulk properties as “Topologically Massive Gravity” but improved boundary properties) is coupled to matter. Consistency requires a particular matter source tensor, which is quadratic in the stress tensor. The consequences are explored for an ideal fluid in the context of asymptotically de-Sitter (dS) cosmological solutions, which bounce smoothly from contraction to expansion. Various vacuum solutions are also found, including warped (A)dS, and (for special values of parameters) static black holes and an (A)dS2 × S 1 vacuum.

An O(D, D) invariant Hamiltonian action for the superstring

We construct O(D, D) invariant actions for the bosonic string and RNS superstring, using Hamiltonian methods and ideas from double field theory. In this framework the doubled coordinates of double field theory appear as coordinates on phase space, and T-duality becomes a canonical transformation. Requiring the algebra of constraints to close leads to the section condition, which splits the phase space coordinates into spacetime coordinates and momenta.

Chern–Simons-Like Gravity Theories

A wide class of three-dimensional gravity models can be put into “Chern–Simons-like” form. We perform a Hamiltonian analysis of the general model and then specialise to Einstein-Cartan Gravity, General Massive Gravity, the recently proposed Zwei-Dreibein Gravity and a further parity violating generalisation combining the latter two.

All Superparticles are BPS

The generic action for an N-extended superparticle in D-dimensional Minkowski spacetime is shown to have ‘hidden’ supersymmetries (related by ‘dualities’ to the manifest supersymmetries) such that the full supersymmetry algebra is BPS-saturated; the exceptions (which include, trivially, the massless case) are those for which the manifest supersymmetry algebra is already BPS-saturated. Moreover, it is shown that any ‘non-BPS’ superparticle action is a gauge-fixed version of the ‘BPS’ superparticle action for which all supersymmetries are manifest. An example is the N = 1 massive D = 10 superparticle, which actually has N = 2 supersymmetry and is equivalent to the action for a D0-brane of IIA superstring theory.

Supertwistors and massive particles

Abstract In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a “spin-shell” constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N -extended space–time supersymmetry) in three and four space–time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N = 1 and BPS-saturated N = 2 superparticle actions. We also find the supertwistor form of the action for “spinning particles” with N -extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N = 2 case.

Twistors and the massive spinning particle

Gauge-invariant twistor variables are found for the massive spinning particle with N-extended local worldline supersymmetry, in spacetime dimensions D=3,4,6. The twistor action is manifestly Lorentz invariant but the anticommuting spin variables appear exactly as in the non-relativistic limit. This allows a simple confirmation that the quantum N=2 spinning particle has either spin one or spin zero, and that N>2 is quantum inconsistent for D=4,6.

The Hamiltonian Form of Topologically Massive Supergravity

We construct a “Chern-Simons-like” action for N = 1 Topologically Massive Supergravity from the Chern-Simons actions of N = 1 Supergravity and Conformal Supergravity. We convert this action into Hamiltonian form and use this to demonstrate that the theory propagates a single massive 2, 3 � supermultiplet.

The third way to 3D gravity

Consistency of Einstein’s gravitational field equation Gμν ∝ Tμν imposes a “conservation condition” on the T-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

Equivalence of 3D spinning string and superstring

A bstractWe perform a light-cone gauge quantization of the Ramond-Ramond sector of the closed spinning string in three spacetime dimensions (3D). The spectrum is Lorentz invariant and identical to that of the 3D Green-Schwarz closed superstring with