2,768 research outputs found
Interactions between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field
Consistent couplings between a massless tensor field with the mixed symmetry
of the Riemann tensor and a massless vector field are analyzed in the framework
of Lagrangian BRST cohomology. Under the assumptions on smoothness, locality,
Lorentz covariance, and Poincare invariance of the deformations, combined with
the requirement that the interacting Lagrangian is at most second-order
derivative, it is proved that there are no consistent cross-interactions
between a single massless tensor field with the mixed symmetry of the Riemann
tensor and one massless vector field.Comment: LaTeX, 24 page
Yes-go cross-couplings in collections of tensor fields with mixed symmetries of the type (3,1) and (2,2)
Under the hypotheses of analyticity, locality, Lorentz covariance, and
Poincare invariance of the deformations, combined with the requirement that the
interaction vertices contain at most two space-time derivatives of the fields,
we investigate the consistent cross-couplings between two collections of tensor
fields with the mixed symmetries of the type (3,1) and (2,2). The computations
are done with the help of the deformation theory based on a cohomological
approach in the context of the antifield-BRST formalism. Our results can be
synthesized in: 1. there appear consistent cross-couplings between the two
types of field collections at order one and two in the coupling constant such
that some of the gauge generators and of the reducibility functions are
deformed, and 2. the existence or not of cross-couplings among different fields
with the mixed symmetry of the Riemann tensor depends on the indefinite or
respectively positive-definite behaviour of the quadratic form defined by the
kinetic terms from the free Lagrangian.Comment: 35 page
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
Parity violating spin-two gauge theories
Nonlinear covariant parity-violating deformations of free spin-two gauge
theory are studied in n>2 spacetime dimensions, using a linearized frame and
spin-connection formalism, for a set of massless spin-two fields. It is shown
that the only such deformations yielding field equations with a second order
quasilinear form are the novel algebra-valued types in n=3 and n=5 dimensions
already found in some recent related work concentrating on lowest order
deformations. The complete form of the deformation to all orders in n=5
dimensions is worked out here and some features of the resulting new
algebra-valued spin-two gauge theory are discussed. In particular, the internal
algebra underlying this theory on 5-dimensional Minkowski space is shown to
cause the energy for the spin-two fields to be of indefinite sign. Finally, a
Kaluza-Klein reduction to n=4 dimensions is derived, giving a parity-violating
nonlinear gauge theory of a coupled set of spin-two, spin-one, and spin-zero
massless fields.Comment: 17 page
BRST cohomological results on the massless tensor field with the mixed symmetry of the Riemann tensor
The basic BRST cohomological properties of a free, massless tensor field with
the mixed symmetry of the Riemann tensor are studied in detail. It is shown
that any non-trivial co-cycle from the local BRST cohomology group can be taken
to stop at antighost number three, its last component belonging to the
cohomology of the exterior longitudinal derivative and containing non-trivial
elements from the (invariant) characteristic cohomology.Comment: 39 page
Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)
The main BRST cohomological properties of a free, massless tensor field that
transforms in an irreducible representation of GL(D,R), corresponding to a
rectangular, two-column Young diagram with k>2 rows are studied in detail. In
particular, it is shown that any non-trivial co-cycle from the local BRST
cohomology group H(s|d) can be taken to stop either at antighost number (k+1)
or k, its last component belonging to the cohomology of the exterior
longitudinal derivative H(gamma) and containing non-trivial elements from the
(invariant) characteristic cohomology H^{inv}(delta|d).Comment: Latex, 50 pages, uses amssym
No cross-interactions among different tensor fields with the mixed symmetry (3,1) intermediated by a vector field
Under the hypotheses of analyticity in the coupling constant, locality,
Lorentz covariance, and Poincare invariance of the deformations, combined with
the preservation of the number of derivatives on each field, the consistent
interactions between a collection of free massless tensor gauge fields with the
mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian
vector field, respectively a -form gauge field, are addressed. The main
result is that a single mixed symmetry tensor field from the collection gets
coupled to the vector field/-form. Our final result resembles to the well
known fact from General Relativity according to which there is one graviton in
a given world.Comment: 19 page
Supersymmetric Higher Spin Theories
We revisit the higher spin extensions of the anti de Sitter algebra in four
dimensions that incorporate internal symmetries and admit representations that
contain fermions, classified long ago by Konstein and Vasiliev. We construct
the , Euclidean and Kleinian version of these algebras, as well as the
corresponding fully nonlinear Vasiliev type higher spin theories, in which the
reality conditions we impose on the master fields play a crucial role. The
supersymmetric higher spin theory in , on which we elaborate
further, is included in this class of models. A subset of Konstein-Vasiliev
algebras are the higher spin extensions of the superalgebras
for mod 4 and can be realized using
fermionic oscillators. We tensor the higher superalgebras of the latter kind
with appropriate internal symmetry groups and show that the mod 4
higher spin algebras are isomorphic to those with mod 4. We
describe the fully nonlinear higher spin theories based on these algebras as
well, and we elaborate further on the supersymmetric theory,
providing two equivalent descriptions one of which exhibits manifestly its
relation to the supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin
Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie
Interactions of a massless tensor field with the mixed symmetry of the Riemann tensor. No-go results
Non-trivial, consistent interactions of a free, massless tensor field t_{\mu
\nu |\alpha \beta} with the mixed symmetry of the Riemann tensor are studied in
the following cases: self-couplings, cross-interactions with a Pauli-Fierz
field and cross-couplings with purely matter theories. The main results,
obtained from BRST cohomological techniques under the assumptions on
smoothness, locality, Lorentz covariance and Poincar\'{e} invariance of the
deformations, combined with the requirement that the interacting Lagrangian is
at most second-order derivative, can be synthesized into: no consistent
self-couplings exist, but a cosmological-like term; no cross-interactions with
the Pauli-Fierz field can be added; no non-trivial consistent cross-couplings
with the matter theories such that the matter fields gain gauge transformations
are allowed.Comment: for version 3: 45 pages, uses amssymb; shortened version, the three
appendices from version 2 can be found in hep-th/040209
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