Interactions in Theories with Mixed Symmetry Tensor Fields: Yes-Go Results

2010 ◽  
Author(s):  
C. Bizdadea ◽  
E. M. Cioroianu ◽  
I. Negru ◽  
S. O. Saliu ◽  
S. C. Sararu ◽  
...  
Keyword(s):  
Tensor Fields ◽  
Mixed Symmetry

Consistent Interactions Involving Dual Formulations of Linearized Gravity in Terms of Massless Tensor Fields with the Mixed Symmetry (k,1)

2011 ◽  
Author(s):  
C. Bizdadea ◽  
E. M. Cioroianu ◽  
M. T. Miaută ◽  
S. O. Saliu ◽  
S. C. Săraru ◽  
...  
Keyword(s):  
Tensor Fields ◽  
Linearized Gravity ◽  
Mixed Symmetry

scholarly journals Mixed Symmetry-Tipe (k,1) Massless Tensor Fields. Consistent Interactions Of Dual Linearized Gravity

2012 ◽  
Vol 56 (1) ◽  
pp. 106-111
Author(s):  
C. Bizdadea ◽  
S. O. Saliu ◽  
M. Toma
Keyword(s):  
Master Equation ◽  
Young Diagram ◽  
Tensor Field ◽  
Local Cohomology ◽  
Tensor Fields ◽  
Linearized Gravity ◽  
Mixed Symmetry

AbstractA particular case of interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k,1) with k=4, dual to linearized gravity in D=7, is considered in the context of: self-couplings, cross-interactions with a Pauli-Fierz field, cross-couplings to purely matter theories, and interactions with an Abelian 1-form. The general approach relies on the deformation of the solution to the master equation from the antifield-BRST formalism by means of the local cohomology of the BRST differential.

Polarization tensor in de Sitter gauge gravity

2021 ◽  
pp. 2150035
Author(s):  
R. Raziani ◽  
M. V. Takook
Keyword(s):  
Tensor Field ◽  
Vector Fields ◽  
Polarization Tensor ◽  
De Sitter ◽  
Field Equations ◽  
Tensor Fields ◽  
Sitter Group ◽  
Generalized Polarization ◽  
Mixed Symmetry ◽  
Symmetry Rank

The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

scholarly journals U-dual branes and mixed symmetry tensor fields

2014 ◽  
Vol 62 (9-10) ◽  
pp. 743-748 ◽  
Author(s):  
A. Chatzistavrakidis ◽  
F.F. Gautason
Keyword(s):  
Tensor Fields ◽  
Mixed Symmetry

scholarly journals On symmetries and dynamics of exotic supermultiplets

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ruben Minasian ◽  
Charles Strickland-Constable ◽  
Yi Zhang
Keyword(s):  
Field Theory ◽  
Extended Supersymmetry ◽  
Degrees Of Freedom ◽  
Three Dimensions ◽  
Tensor Fields ◽  
Time Section ◽  
Mixed Symmetry ◽  
Dimensional Gravity ◽  
M Theory ◽  
Chern Simons

Abstract Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an $$ \mathcal{N} $$ N = (4, 0) multiplet has a four index exotic graviton and it was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M theory compactified on T6. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional field theory, finding in particular that the six-dimensional momenta do not correspond to a conventional space-time section. When compactified on a circle, the six-dimensional multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies (computed using the product multiplets construction) and the generation of Chern-Simons couplings, we find reason to doubt that their dynamics will agree with the five-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular fixed-volume T3-fibered space-times play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity.

scholarly journals YES-GO CROSS-COUPLINGS IN COLLECTIONS OF TENSOR FIELDS WITH MIXED SYMMETRIES OF THE TYPE (3, 1) AND (2, 2)

2010 ◽  
Vol 25 (06) ◽  
pp. 1211-1238
Author(s):  
CONSTANTIN BIZDADEA ◽  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
SOLANGE-ODILE SALIU ◽  
ELENA-MIRELA BĂBĂLÎC
Keyword(s):  
Quadratic Form ◽  
Deformation Theory ◽  
Riemann Tensor ◽  
Positive Definite ◽  
Coupling Constant ◽  
Tensor Fields ◽  
Lorentz Covariance ◽  
Mixed Symmetry ◽  
Type 3 ◽  
Derivatives Of

Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincaré 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: (i) 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 (ii) 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 behavior of the quadratic form defined by the kinetic terms from the free Lagrangian.

On Horizontal and Complete Lifts of $(1,1)\;$ Tensor Fields F Satisfying ${f(2K+S,S)=0}$

2016 ◽  
Vol 6 (1) ◽  
pp. 143
Author(s):  
Abhishek Singh ◽  
Ramesh Kumar Pandey ◽  
Sachin Khare
Keyword(s):  
Tensor Fields

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

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