Minimal massive 3D gravity unitarity redux

A geometrical analysis of the bulk and anti-de Sitter boundary unitarity conditions of 3D “Minimal Massive Gravity” (MMG) (which evades the “bulk/boundary clash” of Topologically Massive Gravity) is used to extend and simplify previous results, showing that unitarity selects, up to equivalence, a connected region in parameter space. We also initiate the study of flat-space holography for MMG.A.S.A. and P.K.T. acknowledge support from the UK Science and Technology Facilities Council (grant ST/L000385/1). A.S.A. also acknowledges support from Clare Hall College, Cambridge, and from the Cambridge Trust. We are grateful to Eduardo Casali, Elias Kiritsis and Alasdair Routh for helpful discussions, and to Eric Bergshoeff and Wout Merbis for helpful correspondence.This is the final version of the article. It was first published by IOP at https://camacuk.zendesk.com/agent/tickets/626

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.LM acknowledges partial support from the National Science Foundation Award PHY-1214521. PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society, and he thanks the University of Groningen for hospitality during the writing of this paper. LM and PKT are grateful for the hospitality of the Pedro Pascual Benasque Center for Science, where part of this work was done.This is the final version of the article. It first appeared from IOP via http://dx.doi.org/10.1088/1751-8113/49/2/02540

On-shell versus off-shell equivalence in 3D gravity

A given field theory action determines a set of field equations but other actions may yield equivalent field equations; if so they are on-shell equivalent. They may also be off-shell equivalent, being related by the elimination of auxiliary fields or by local field redefinitions, but this is not guaranteed, as we demonstrate by consideration of the linearized limit of 3D massive gravity models. Failure to appreciate this subtlety has led to incorrect conclusions in recent studies of the ``Minimal Massive Gravity'' model

Twistor description of spinning particles in AdS

The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D=4,5,7, which linearises invariance under the AdS isometry group Sp(4;K) for K=R,C,H,, is generalized to the massless N-extended ``spinning particle''. The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS5

The third way to 3D gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-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. AJR is supported by a grant from the London Mathematical Society, and he would also like to thank the University of Groningen for hospitality during the writing of this essay.This is the author accepted manuscript. The final version is available from World Scientific via http://dx.doi.org/10.1142/S021827181544015

Late-time cosmic acceleration from compactification

We investigate the implications of energy conditions on cosmological compactification solutions of the higher-dimensional Einstein field equations. It is known that the Strong Energy Condition forbids time-independent compactifications to de Sitter space but allows time-dependent compactifications to other (homogeneous and isotropic) expanding universes that undergo a transient period of acceleration. Here we show that the same assumptions allow compactification to FLRW universes undergoing late-time accelerated expansion; the late-time stress tensor is a perfect fluid but with a lower bound on the pressure/energy-density ratio that excludes de Sitter but allows accelerated power-law expansion. The compact space undergoes a decelerating expansion that leads to decompactification, but on an arbitrarily long timescale

The Galilean superstring

The action for a Galilean superstring is found from a non-relativistic limit of the closed Green-Schwarz (GS) superstring; it has zero tension and provides an example of a massless super-Galilean system. A Wess-Zumino term leads to a topological central charge in the Galilean supersymmetry algebra, such that unitarity requires a upper bound on the total momentum. This Galilean-invariant bound, which is also implied by the classical phase-space constraints, is saturated by solutions of the superstring equations of motion that half-preserve supersymmetry. We discuss briefly the extension to the Galilean supermembrane.The material in it is based upon work supported in part by the National Science Foun- dation under Grant Number PHY-1620610 and with support from The Robert A. Welch Foundation, Grant No. F-0014. J.G also has been supported by FPA2013-46570-C2-1-P, 2014-SGR-104 (Generalitat de Catalunya) and Consolider CPAN and by the Spanish gover- ment (MINECO/FEDER) under project MDM-2014-0369 of ICCUB (Unidad de Excelencia María de Maeztu). PKT acknowledges support from the U.K. Science and Technology Facilities Council (grant ST/L000385/1)

Worldline CPT and massless supermultiplets

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the $\mathscr{N}$-extended superparticle is shown to be anomalous when $\mathscr{N}$ is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral $\textbf{U(1)}$ gauge invariance. This accords with the fact that no massless $\mathscr{N}$=1 super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when $\mathscr{N}$ is even, but it has $\textbf{2}$$^{\mathscr{N}+1}$ states when $\frac{1}{2}$$\mathscr{N}$ is odd (e.g. the $\mathscr{N}$=2 hypermultiplet) in contrast to just $\textbf{2}$$^{\mathscr{N}}$ when $\frac{1}{2}$$\mathscr{N}$ is even (e.g. the $\mathscr{N}$=4 Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when $\frac{1}{2}$$\mathscr{N}$ is odd.A.S. Arvanitakis and P. K. Townsend acknowledge support from the UK Science and Technology Facilities Council (grant ST/L000385/1).A.S. Arvanitakis also acknowledges support from Clare Hall College, Cambridge, and from the Cambridge Trust

Pauli-Lubanski, supertwistors, and the superspinning particle

We present a novel construction of the super-Pauli-Lubanski pseudo-vector for 4D supersymmetry and show how it arises naturally from the spin-shell constraints in the supertwistor formulation of superparticle dynamics. We illustrate this result in the context of a simple classical action for a “superspinning particle” of superspin 1/2. We then use an Sl(2;K)-spinor formalism for K=ℝ,ℂ,ℍ to unify our 4D results with previous results for 3D and 6D

Gravity and the spin-2 planar Schroedinger equation

A Schroedinger equation proposed for the GMP gapped spin-2 mode of fractional Quantum Hall states is found from a novel non-relativistic 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 non-linear Einstein equations, a confining harmonic oscillator potential for the individual particles