61 research outputs found
Nonlinear Dynamics of Parity-Even Tricritical Gravity in Three and Four Dimensions
Recently proposed "multicritical" higher-derivative gravities in Anti de
Sitter space carry logarithmic representations of the Anti de Sitter isometry
group. While generically non-unitary already at the quadratic, free-theory
level, in special cases these theories admit a unitary subspace. The simplest
example of such behavior is "tricritical" gravity. In this paper, we extend the
study of parity-even tricritical gravity in d = 3, 4 to the first nonlinear
order. We show that the would-be unitary subspace suffers from a linearization
instability and is absent in the full non-linear theory.Comment: 22 pages; v2: references added, published versio
On unitary subsectors of polycritical gravities
We study higher-derivative gravity theories in arbitrary space-time dimension
d with a cosmological constant at their maximally critical points where the
masses of all linearized perturbations vanish. These theories have been
conjectured to be dual to logarithmic conformal field theories in the
(d-1)-dimensional boundary of an AdS solution. We determine the structure of
the linearized perturbations and their boundary fall-off behaviour. The
linearized modes exhibit the expected Jordan block structure and their inner
products are shown to be those of a non-unitary theory. We demonstrate the
existence of consistent unitary truncations of the polycritical gravity theory
at the linearized level for odd rank.Comment: 22 pages. Added references, rephrased introduction slightly.
Published versio
The supermultiplet of boundary conditions in supergravity
Boundary conditions in supergravity on a manifold with boundary relate the
bulk gravitino to the boundary supercurrent, and the normal derivative of the
bulk metric to the boundary energy-momentum tensor. In the 3D N=1 setting, we
show that these boundary conditions can be stated in a manifestly
supersymmetric form. We identify the Extrinsic Curvature Tensor Multiplet, and
show that boundary conditions set it equal to (a conjugate of) the boundary
supercurrent multiplet. Extension of our results to higher-dimensional models
(including the Randall-Sundrum and Horava-Witten scenarios) is discussed.Comment: 22 pages. JHEP format; references added; published versio
Effective Lagrangian from Higher Curvature Terms: Absence of vDVZ Discontinuity in AdS Space
We argue that the van Dam-Veltman-Zakharov discontinuity arising in the limit of the massive graviton through an explicit Pauli-Fierz mass term
could be absent in anti de Sitter space. This is possible if the graviton can
acquire mass spontaneously from the higher curvature terms or/and the massless
limit is attained faster than the cosmological constant . We discuss the effects of higher-curvature couplings and of an explicit
cosmological term () on stability of such continuity and of massive
excitations.Comment: 23 pages, Latex, the version to appear in Class. Quant. Gra
MacDowell-Mansouri gravity and Cartan geometry
The geometric content of the MacDowell-Mansouri formulation of general
relativity is best understood in terms of Cartan geometry. In particular,
Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick
of combining the Levi-Civita connection and coframe field, or soldering form,
into a single physical field. The Cartan perspective allows us to view physical
spacetime as tangentially approximated by an arbitrary homogeneous "model
spacetime", including not only the flat Minkowski model, as is implicitly used
in standard general relativity, but also de Sitter, anti de Sitter, or other
models. A "Cartan connection" gives a prescription for parallel transport from
one "tangent model spacetime" to another, along any path, giving a natural
interpretation of the MacDowell-Mansouri connection as "rolling" the model
spacetime along physical spacetime. I explain Cartan geometry, and "Cartan
gauge theory", in which the gauge field is replaced by a Cartan connection. In
particular, I discuss MacDowell-Mansouri gravity, as well as its more recent
reformulation in terms of BF theory, in the context of Cartan geometry.Comment: 34 pages, 5 figures. v2: many clarifications, typos correcte
Domain wall brane in squared curvature gravity
We suggest a thick braneworld model in the squared curvature gravity theory.
Despite the appearance of higher order derivatives, the localization of gravity
and various bulk matter fields is shown to be possible. The existence of the
normalizable gravitational zero mode indicates that our four-dimensional
gravity is reproduced. In order to localize the chiral fermions on the brane,
two types of coupling between the fermions and the brane forming scalar is
introduced. The first coupling leads us to a Schr\"odinger equation with a
volcano potential, and the other a P\"oschl-Teller potential. In both cases,
the zero mode exists only for the left-hand fermions. Several massive KK states
of the fermions can be trapped on the brane, either as resonant states or as
bound states.Comment: 18 pages, 5 figures and 1 table, references added, improved version
to be published in JHE
Exploring Curved Superspace
We systematically analyze Riemannian manifolds M that admit rigid
supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R
symmetry. We find that M admits a single supercharge, if and only if it is a
Hermitian manifold. The supercharge transforms as a scalar on M. We then
consider the restrictions imposed by the presence of additional supercharges.
Two supercharges of opposite R-charge exist on certain fibrations of a
two-torus over a Riemann surface. Upon dimensional reduction, these give rise
to an interesting class of supersymmetric geometries in three dimensions. We
further show that compact manifolds admitting two supercharges of equal
R-charge must be hyperhermitian. Finally, four supercharges imply that M is
locally isometric to M_3 x R, where M_3 is a maximally symmetric space.Comment: 39 pages; minor change
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
The post-Minkowskian limit of f(R)-gravity
We formally discuss the post-Minkowskian limit of
-gravity without adopting conformal transformations but developing all
the calculations in the original Jordan frame. It is shown that such an
approach gives rise, in general, together with the standard massless graviton,
to massive scalar modes whose masses are directly related to the analytic
parameters of the theory. In this sense, the presence of massless gravitons
only is a peculiar feature of General Relativity. This fact is never stressed
enough and could have dramatic consequences in detection of gravitational
waves. Finally the role of curvature stress-energy tensor of -gravity is
discussed showing that it generalizes the so called Landau-Lifshitz tensor of
General Relativity. The further degrees of freedom, giving rise to the massive
modes, are directly related to the structure of such a tensor.Comment: 9 page
Projective Invariance and One-Loop Effective Action in Affine-Metric Gravity Interacting with Scalar Field
We investigate the influence of the projective invariance on the
renormalization properties of the theory. One-loop counterterms are calculated
in the most general case of interaction of gravity with scalar field.Comment: 10 pages, LATE
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