On Unitarity of Massive Gravity in Three Dimensions

We examine a unitarity of a particular higher-derivative extension of general relativity in three space-time dimensions, which has been recently shown to be equivalent to the Pauli-Fierz massive gravity at the linearized approximation level, and explore a possibility of generalizing the model to higher space-time dimensions. We find that the model in three dimensions is indeed unitary in the tree-level, but the corresponding model in higher dimensions is not so due to the appearance of non-unitary massless spin-2 modes.Comment: 10 pages, references adde

Aspects of a supersymmetric Brans-Dicke theory

We consider a locally supersymmetric theory where the Planck mass is replaced by a dynamical superfield. This model can be thought of as the Minimal Supersymmetric extension of the Brans-Dicke theory (MSBD). The motivation that underlies this analysis is the research of possible connections between Dark Energy models based on Brans-Dicke-like theories and supersymmetric Dark Matter scenarios. We find that the phenomenology associated with the MSBD model is very different compared to the one of the original Brans-Dicke theory: the gravitational sector does not couple to the matter sector in a universal metric way. This feature could make the minimal supersymmetric extension of the BD idea phenomenologically inconsistent.Comment: 6 pages, one section is adde

Helicity-1/2 Mode as a Probe of Interactions of Massive Rarita-Schwinger Field

We consider the electromagnetic and gravitational interactions of a massive Rarita-Schwinger field. Stueckelberg analysis of the system, when coupled to electromagnetism in flat space or to gravity, reveals in either case that the effective field theory has a model-independent upper bound on its UV cutoff, which is finite but parametrically larger than the particle's mass. It is the helicity-1/2 mode that becomes strongly coupled at the cutoff scale. If the interactions are inconsistent, the same mode becomes a telltale sign of pathologies. Alternatively, consistent interactions are those that propagate this mode within the light cone. Studying its dynamics not only sheds light on the Velo-Zwanziger acausality, but also elucidates why supergravity and other known consistent models are pathology-free.Comment: 18 pages, cutoff analysis improved, to appear in PR

The mass of the graviton and the cosmological constant

We show that the graviton acquires a mass in a de Sitter background given by $m_{g}^{2}=-{2/3}\Lambda.$ This is precisely the fine-tuning value required for the perturbed gravitational field to mantain its two degrees of freedom.Comment: Title changed and few details added, without any changes in the conclusio

An equivalence principle for scalar forces

The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent attempts to modify gravity at cosmological distances. Although a universal scalar-matter coupling is not mandatory, once postulated, it is stable against classical and quantum renormalizations in the matter sector. The coupling strength itself is subject to renormalization of course. The scalar equivalence principle is violated only for objects for which either the graviton self-interaction or the scalar self-interaction is important---the first applies to black holes, while the second type of violation is avoided if the scalar is Galilean-symmetric.Comment: 4 pages, 1 figur

Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD

The order parameter of a finite system with a spontaneously broken continuous global symmetry acts as a quantum mechanical rotor. Both antiferromagnets with a spontaneously broken $SU(2)_s$ spin symmetry and massless QCD with a broken $SU(2)_L \times SU(2)_R$ chiral symmetry have rotor spectra when considered in a finite volume. When an electron or hole is doped into an antiferromagnet or when a nucleon is propagating through the QCD vacuum, a Berry phase arises from a monopole field and the angular momentum of the rotor is quantized in half-integer units.Comment: 4 page

Topological Aspect of high-TcT_c Superconductivity, Fractional Quantum Hall Effect and Berry Phase

We have analysed here the equivalence of RVB states with $\nu=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $\nu=1/2$.Comment: 12 pages latex fil

Fully Covariant Van Dam-Veltman-Zakharov Discontinuity, and Absence Thereof

In both old and recent literature, it has been argued that the celebrated van Dam-Veltman-Zakharov (vDVZ) discontinuity of massive gravity is an artifact due to linearization of the true equations of motion. In this letter, we investigate that claim. First, we exhibit an explicit -albeit somewhat arbitrary- fully covariant set of equations of motion that, upon linearization, reduce to the standard Pauli-Fierz equations. We show that the vDVZ discontinuity still persists in that non-linear, covariant theory. Then, we restrict our attention to a particular system that consistently incorporates massive gravity: the Dvali-Gabadadze-Porrati (DGP) model. DGP is fully covariant and does not share the arbitrariness and imperfections of our previous covariantization, and its linearization exhibits a vDVZ discontinuity. Nevertheless, we explicitly show that the discontinuity does disappear in the fully covariant theory, and we explain the reason for this phenomenon.Comment: Inconsequential mistakes in Eqs. (12,13,20) corrected. 10 pages, Latex. To appear in Physics Letters

Dual descriptions of spin two massive particles in D=2+1D=2+1 via master actions

In the first part of this work we show the decoupling (up to contact terms) of redundant degrees of freedom which appear in the covariant description of spin two massive particles in $D=2+1$. We make use of a master action which interpolates, without solving any constraints, between a first, second and third order (in derivatives) self-dual model. An explicit dual map between those models is derived. In our approach the absence of ghosts in the third order self-dual model, which corresponds to a quadratic truncation of topologically massive gravity, is due to the triviality (no particle content) of the Einstein-Hilbert action in $D=2+1$. In the second part of the work, also in $D=2+1$, we prove the quantum equivalence of the gauge invariant sector of a couple of self-dual models of opposite helicities (+2 and -2) and masses $m_+$ and $m_-$ to a generalized self-dual model which contains a quadratic Einstein-Hilbert action, a Chern-Simons term of first order and a Fierz-Pauli mass term. The use of a first order Chern-Simons term instead of a third order one avoids conflicts with the sign of the Einstein-Hilbert action.Comment: title and abstract slightly modified, 3 references added, comments on interactions include

An Exotic Theory of Massless Spin-Two Fields in Three Dimensions

It is a general belief that the only possible way to consistently deform the Pauli-Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one allows for PT non-invariant terms. The new gauge algebra is different from that of diffeomorphisms. Furthermore, this deformation can be generalized to the case of a collection of massless spin-two fields. In this case it describes a consistent interaction among them.Comment: 21+1 pages. Minor corrections and reference adde