40 research outputs found
Monopoles for Gravitation and for Higher Spin Fields
We consider massless higher spin gauge theories with both electric and
magnetic sources, with a special emphasis on the spin two case. We write the
equations of motion at the linear level (with conserved external sources) and
introduce Dirac strings so as to derive the equations from a variational
principle. We then derive a quantization condition that generalizes the
familiar Dirac quantization condition, and which involves the conserved charges
associated with the asymptotic symmetries for higher spins. Next we discuss
briefly how the result extends to the non linear theory. This is done in the
context of gravitation, where the Taub-NUT solution provides the exact solution
of the field equations with both types of sources. We rederive, in analogy with
electromagnetism, the quantization condition from the quantization of the
angular momentum. We also observe that the Taub-NUT metric is asymptotically
flat at spatial infinity in the sense of Regge and Teitelboim (including their
parity conditions). It follows, in particular, that one can consistently
consider in the variational principle configurations with different electric
and magnetic masses.Comment: 24 page
Simple compactifications and Black p-branes in Gauss-Bonnet and Lovelock Theories
We look for the existence of asymptotically flat simple compactifications of
the form in -dimensional gravity theories with higher
powers of the curvature. Assuming the manifold to be spherically
symmetric, it is shown that the Einstein-Gauss-Bonnet theory admits this class
of solutions only for the pure Einstein-Hilbert or Gauss-Bonnet Lagrangians,
but not for an arbitrary linear combination of them. Once these special cases
have been selected, the requirement of spherical symmetry is no longer relevant
since actually any solution of the pure Einstein or pure Gauss-Bonnet theories
can then be toroidally extended to higher dimensions. Depending on and the
spacetime dimension, the metric on may describe a black hole or a
spacetime with a conical singularity, so that the whole spacetime describes a
black or a cosmic -brane, respectively. For the purely Gauss-Bonnet theory
it is shown that, if is four-dimensional, a new exotic class of black
hole solutions exists, for which spherical symmetry can be relaxed.
Under the same assumptions, it is also shown that simple compactifications
acquire a similar structure for a wide class of theories among the Lovelock
family which accepts this toroidal extension.
The thermodynamics of black -branes is also discussed, and it is shown
that a thermodynamical analogue of the Gregory-Laflamme transition always
occurs regardless the spacetime dimension or the theory considered, hence not
only for General Relativity.
Relaxing the asymptotically flat behavior, it is also shown that exact black
brane solutions exist within a very special class of Lovelock theories.Comment: 30 pages, no figures, few typos fixed, references added, final
version for JHE
Master Higher-Spin Particle
We propose a "master" higher-spin (HS) particle system. The particle model
relevant to the unfolded formulation of HS theory, as well as the HS particle
model with a bosonic counterpart of supersymmetry, follow from the master model
as its two different gauges. Quantization of the master system gives rise to a
new form of the massless HS equations in an extended space involving, besides
extra spinorial coordinates, also a complex scalar one. As solutions to these
equations we recover the massless HS multiplet with fields of all integer and
half-integer helicities, and obtain new multiplets with a non-zero minimal
helicity. The HS multiplets are described by complex wave functions which are
holomorphic in the scalar coordinate and carry an extra U(1) charge q. The
latter fully characterizes the given multiplet by fixing the minimal helicity
as q/2. We construct a twistorial formulation of the master system and present
the general solution of the associate HS equations through an unconstrained
twistor "prepotential".Comment: 21 pages, minor corrections, version to appear in Class. Quantum Gra
Consistent deformations of [p,p]-type gauge field theories
Using BRST-cohomological techniques, we analyze the consistent deformations
of theories describing free tensor gauge fields whose symmetries are
represented by Young tableaux made of two columns of equal length p, p>1. Under
the assumptions of locality and Poincare invariance, we find that there is no
consistent deformation of these theories that non-trivially modifies the gauge
algebra and/or the gauge transformations. Adding the requirement that the
deformation contains no more than two derivatives, the only possible
deformation is a cosmological-constant-like term.Comment: 17 pages, details of a proof added, accepted for publication in JHE
Propagating modes of non-Abelian tensor gauge field of second rank
In the recently proposed extension of the YM theory, non-Abelian tensor gauge
field of the second rank is represented by a general tensor whose symmetric
part describes the propagation of charged gauge boson of helicity two and its
antisymmetric part - the helicity zero charged gauge boson. On the
non-interacting level these polarizations are similar to the polarizations of
the graviton and of the Abelian antisymmetric B field, but the interaction of
these gauge bosons carrying non-commutative internal charges cannot be directly
identified with the interaction of gravitons or B field. Our intention here is
to illustrate this result from different perspectives which would include
Bianchi identity for the corresponding field strength tensor and the analysis
of the second-order partial differential equation which describes in this
theory the propagation of non-Abelian tensor gauge field of the second rank.Comment: 22 pages, Latex fil
On gravitational interactions for massive higher spins in
In this paper we investigate gravitational interactions of massive higher
spin fields in three dimensional space with arbitrary value of
cosmological constant including flat Minkowski space. We use frame-like gauge
description for such massive fields adopted to three-dimensional case. At
first, we carefully analyze the procedure of switching on gravitational
interactions in the linear approximation on the example of massive spin-3 field
and then proceed with the generalization to the case of arbitrary integer spin
field. As a result we construct a cubic interaction vertex linear in spin-2
field and quadratic in higher spin field on background. As in the
massless case the vertex does not contain any higher derivative corrections to
the Lagrangian and/or gauge transformations. Thus, even after switching on
gravitational interactions, one can freely consider any massless or partially
massless limits as well as the flat one.Comment: 21 pages. Some clarifications and 1 new reference added. Version to
appear in the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT"
edited by Matthias Gaberdiel and Mikhail Vasilie
A note on spin-s duality
Duality is investigated for higher spin (), free, massless, bosonic
gauge fields. We show how the dual formulations can be derived from a common
"parent", first-order action. This goes beyond most of the previous treatments
where higher-spin duality was investigated at the level of the equations of
motion only. In D=4 spacetime dimensions, the dual theories turn out to be
described by the same Pauli-Fierz (s=2) or Fronsdal () action (as it
is the case for spin 1). In the particular s=2 D=5 case, the Pauli-Fierz action
and the Curtright action are shown to be related through duality. A crucial
ingredient of the analysis is given by the first-order, gauge-like,
reformulation of higher spin theories due to Vasiliev.Comment: Minor corrections, reference adde
On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
An almost brief, though lengthy, review introduction about the long history
of higher order gravities and their applications, as employed in the
literature, is provided. We review the analogous procedure between higher order
gravities and GR, as described in our previous works, in order to highlight its
important achievements. Amongst which are presentation of an easy
classification of higher order Lagrangians and its employment as a
\emph{criteria} in order to distinguish correct metric theories of gravity. For
example, it does not permit the inclusion of only one of the second order
Lagrangians in \emph{isolation}. But, it does allow the inclusion of the
cosmological term. We also discuss on the compatibility of our procedure and
the Mach idea. We derive a dimensional dependent version of Duff's trace
anomaly relation, which in \emph{four}-dimension is the same as the usual Duff
relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any}
dimension. The square of the Weyl tensor identically satisfies it independent
of dimension, however, this Lagrangian satisfies the previous relation only in
three and four dimensions.Comment: 30 pages, added reference