arXiv subjects
Publications and source records attributed to Paul K. Townsend.
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.
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 x S1 vacuum.
We present an alternative to Topologically Massive Gravity (TMG) with the same "minimal" bulk properties; i.e. a single local degree of freedom that is realized as a massive graviton in linearization about an anti-de Sitter (AdS) vacuum. However, in contrast to TMG, the new "minimal massive gravity" has both a positive energy graviton and positive central charges for the asymptotic AdS-boundary conformal algebra.
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 spacetime 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.
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.
We present a generally-covariant and parity-invariant "zwei-dreibein" action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models, and extends them, in the context of the AdS/CFT correspondence, to allow for a positive central charge consistent with bulk unitarity.
We perform a light-cone gauge quantization of the Ramond 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 ${\cal N}=2$ space-time supersymmetry, quantized in light-cone gauge.
A number of three-dimensional (3D) gravity models, such as 3D conformal gravity, admit "exotic" black hole solutions: the metric is the same as the BTZ metric of 3D Einstein gravity but with reversed roles for mass and angular momentum, and an entropy proportional to the length of the inner horizon instead of the event horizon. Here we show that the BTZ solutions of the "exotic" 3D Einstein gravity (with parity-odd action but Einstein field equations) are exotic black holes, and we investigate their thermodynamics. The first and second laws of black hole thermodynamics still apply, and the entropy still has a statistical interpretation.
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 "new topologically massive gravity", which therefore suffers from a linearization instability.
We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schroedinger model.
A 6th-order, but ghost-free, gauge-invariant action is found for a 4th-rank symmetric tensor potential in a three-dimensional (3D) Minkowski spacetime. It propagates two massive modes of spin 4 that are interchanged by parity, and is thus a spin-4 analog of linearized "new massive gravity". Also found are ghost-free spin-4 analogs of linearized "topologically massive gravity" and "new topologically massive gravity", of 5th- and 8th-order respectively.
We explain how fractional spin and statistics are relevant to (super)strings in a three-dimensional (3D) Minkowski spacetime.
The classical Green-Schwarz superstring action, with N=1 or N=2 spacetime supersymmetry, exists for spacetime dimensions D=3,4,6,10, but quantization in the light-cone gauge breaks Lorentz invariance unless either D=10, which leads to critical superstring theory, or D=3. We give details of results presented previously for the bosonic and N=1 closed 3D (super)strings and extend them to the N=2 3D superstring. In all cases, the spectrum is parity-invariant and contains anyons of irrational spin.
The physical modes of a recently proposed D-dimensional "critical gravity", linearized about its anti-de Sitter vacuum, are investigated. All "log mode" solutions, which we categorize as `spin 2' or `Proca', arise as limits of the massive spin 2 modes of the non-critical theory. The linearized Einstein tensor of a spin 2 log mode is itself a 'non-gauge' solution of the linearized Einstein equations whereas the linearized Einstein tensor of a Proca mode takes the form of a linearized general coordinate transformation. Our results suggest the existence of a holographically dual logarithmic conformal field theory.
The minimal (${\cal N}=1$) superparticle in three spacetime dimensions (3D) is quantized. For non-zero mass it describes a spin-1/4 semion supermultiplet of "relativistic helicities" (-1/4, 1/4). The addition of a parity-violating Lorentz-Wess-Zumino term shifts this to $(β-1/4,β+1/4)$ for arbitrary $β$. For zero mass, in which case spin is not defined, the quantum superparticle describes a supermultiplet of one boson and one fermion.
Completing earlier work on three dimensional (3D) N=1 supergravity with curvature-squared terms, we construct the general supergravity extension of cosmological massive gravity theories. We expand about supersymmetric anti-de Sitter vacua, finding the conditions for bulk unitarity and the critical points in parameter space at which the spectrum changes. We discuss implications for the dual conformal field theory.
We review the status of three-dimensional "general massive gravity" (GMG) in its linearization about an anti-de Sitter (adS) vacuum, focusing on critical points in parameter space that yield generalizations of "chiral gravity". We then show how these results extend to N=1 super-GMG, expanded about a supersymmetric adS vacuum, and also to the most general `curvature-squared' N=1 supergravity model.
The Bogomolnyi vortex of the N=2 supersymmetric abelian-Higgs model in 2+1 dimensions is shown to be a ``semion'' of spin 1/4. Specifically, the effective superparticle action for one vortex is shown to describe, upon quantization, a parity self-dual centrally-charged `short' supermultiplet of ``relativistic helicities'' (-1/4,-1/4, 1/4,1/4).