Gravitons in Flatland

We review some features of three-dimensional (3D) massive gravity theories. In particular, we stress the role of the Schouten tensor, explore an analogy with Lovelock gravity and discuss renormalizabilty.Comment: 11 pages, Contribution to proceedings of the workshop {\it Cosmology, the Quantum Vacuum and Zeta Functions} in celebration of the 60th birthday of Emilio Elizalde; Barcelona, 8-10 March, 2010. Additional references in v

Massive Gravity in Three Dimensions

A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model, which also includes `topologically-massive' gravity as a special case, propagates the two spin 2 helicity states with different masses. We discuss the extension to massive ${\cal N}$-extended supergravity, and we present a `cosmological' extension that admits an anti-de Sitter vacuum.Comment: Minor corrections plus a further correction to discussion of supersymmetry in adS vacua, Version to be publishe

Hidden supersymmetry of domain walls and cosmologies

We show that all domain-wall solutions of gravity coupled to scalar fields for which the worldvolume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution. By analytic continuation, all flat or closed FLRW cosmologies are shown to satisfy similar first-order equations arising from the existence of ``pseudo-Killing'' spinors.Comment: 4 pages, v2:minor improvements, refs added, version to appear in PR

More on Massive 3D Gravity

We explore the space of static solutions of the recently discovered three-dimensional `New Massive Gravity' (NMG), allowing for either sign of the Einstein-Hilbert term and a cosmological term parametrized by a dimensionless constant $\lambda$. For $\lambda=-1$ we find black hole solutions asymptotic (but not isometric) to the unique (anti) de Sitter vacuum, including extremal black holes that interpolate between this vacuum and (a)dS$_2 \times S^1$. We also investigate unitarity of linearized NMG in (a)dS vacua. We find unitary theories for some dS vacua, but (bulk) unitarity in adS implies negative central charge of the dual CFT, except for $\lambda=3$ where the central charge vanishes and the bulk gravitons are replaced by `massive photons'. A similar phenomenon is found in the massless limit of NMG, for which the linearized equations become equivalent to Maxwell's equations.Comment: 25 pages, 4 figures; v2: minor improvements and extensions, references added; v3: version to appear in PR

Hamilton-Jacobi method for Domain Walls and Cosmologies

We use Hamiltonian methods to study curved domain walls and cosmologies. This leads naturally to first order equations for all domain walls and cosmologies foliated by slices of maximal symmetry. For Minkowski and AdS-sliced domain walls (flat and closed FLRW cosmologies) we recover a recent result concerning their (pseudo)supersymmetry. We show how domain-wall stability is consistent with the instability of adS vacua that violate the Breitenlohner-Freedman bound. We also explore the relationship to Hamilton-Jacobi theory and compute the wave-function of a 3-dimensional closed universe evolving towards de Sitter spacetime.Comment: 18 pages; v2: typos corrected, one ref added, version to appear in PR

Dilaton Domain Walls and Dynamical Systems

Domain wall solutions of $d$-dimensional gravity coupled to a dilaton field $\sigma$ with an exponential potential $\Lambda e^{-\lambda\sigma}$ are shown to be governed by an autonomous dynamical system, with a transcritical bifurcation as a function of the parameter $\lambda$ when $\Lambda<0$. All phase-plane trajectories are found exactly for $\lambda=0$, including separatrices corresponding to walls that interpolate between $adS_d$ and adS_{d-1} \times\bR, and the exact solution is found for $d=3$. Janus-type solutions are interpreted as marginal bound states of these ``separatrix walls''. All flat domain wall solutions, which are given exactly for any $\lambda$, are shown to be supersymmetric for some superpotential $W$, determined by the solution.Comment: 30 pp, 11 figs, significant revision of original. Minor additional corrections in version to appear in journa

Staying true with the help of others: doxastic self-control through interpersonal commitment

I explore the possibility and rationality of interpersonal mechanisms of doxastic self-control, that is, ways in which individuals can make use of other people in order to get themselves to stick to their beliefs. I look, in particular, at two ways in which people can make interpersonal epistemic commitments, and thereby willingly undertake accountability to others, in order to get themselves to maintain their beliefs in the face of anticipated “epistemic temptations”. The first way is through the avowal of belief, and the second is through the establishment of collective belief. I argue that both of these forms of interpersonal epistemic commitment can function as effective tools for doxastic self-control, and, moreover, that the control they facilitate should not be dismissed as irrational from an epistemic perspective

On higher derivatives in 3D gravity and higher-spin gauge theories

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their "self-dual" limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the "extended Chern-Simons" term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for "self-dual" spin 3.Comment: 23 pp. New references, improved spin-3 discussion. Minor additional corrections in v

On massive gravitons in 2+1 dimensions

The Fierz-Pauli (FP) free field theory for massive spin 2 particles can be extended, in a spacetime of (1+2) dimensions (3D), to a generally covariant parity-preserving interacting field theory, in at least two ways. One is "new massive gravity" (NMG), with an action that involves curvature-squared terms. Another is 3D "bigravity", which involves non-linear couplings of the FP tensor field to 3D Einstein-Hilbert gravity. We review the proof of the linearized equivalence of both "massive 3D gravity" theories to FP theory, and we comment on their similarities and differences.Comment: 6 pages, to appear in the proceedings of the Spanish Relativity Meeting ERE2009, Bilbao; minor changes, reference adde