UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

scholarly journals A model for massless higher spin field interacting with a geometrical background

2015 ◽  
Vol 12 (05) ◽  
pp. 1550054
Author(s):  
Giuseppe Bandelloni
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Theory Model ◽  
Algebraic Field ◽  
Spin Field ◽  
Higher Spin ◽  
A Chain ◽  
Equations Of Motions

We study a very general four-dimensional field theory model describing the dynamics of a massless higher spin N symmetric tensor field particle interacting with a geometrical background. This model is invariant under the action of an extended linear diffeomorphism. We investigate the consistency of the equations of motion, and the highest spin degrees of freedom are extracted by means of a set of covariant constraints. Moreover, the highest spin equations of motions (and in general all the highest spin field 1-PI irreducible Green functions) are invariant under a chain of transformations induced by a set of N - 2 Ward operators, while the auxiliary fields equations of motion spoil this symmetry. The first steps to a quantum extension of the model are discussed on the basis of the algebraic field theory. Technical aspects are reported in Appendices, in particular, one of them is devoted to illustrate the spin-2 case.

scholarly journals ON MANIFOLDS ADMITTING THE CONSISTENT LAGRANGIAN FORMULATION FOR HIGHER SPIN FIELDS

2011 ◽  
Vol 26 (16) ◽  
pp. 1183-1196 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
V. A. KRYKHTIN ◽  
P. M. LAVROV
Keyword(s):  
Constant Curvature ◽  
Transversality Condition ◽  
Symmetric Tensor ◽  
Lagrangian Formulation ◽  
Tensor Fields ◽  
Rank Tensor ◽  
Higher Spin ◽  
Spin Fields ◽  
Constant Curvature Space ◽  
Background Fields

We study a possibility of Lagrangian formulation for free massive higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third-rank tensor fields in the framework of BRST approach. Assuming analytical dependence on the mass, curvatures and the other background fields in the Lagrangian and using the most general linearized ansatz for transversality condition, we prove that the consistent formulation is possible only in constant curvature space and that there is only a trivial possibility to include the vector and third-rank tensor in the theory. This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.

THE MODIFIED BARGMANN-WIGNER FORMALISM FOR HIGHER SPIN FIELDS AND RELATIVISTIC QUANTUM MECHANICS

2011 ◽  
Vol 03 ◽  
pp. 121-132 ◽  
Author(s):  
VALERIY V. DVOEGLAZOV
Keyword(s):  
Relativistic Quantum ◽  
Standard Procedure ◽  
Symmetric Tensor ◽  
Riemann Tensor ◽  
Relativistic Quantum Mechanics ◽  
Dynamical Equations ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spins ◽  
Dirac Formalism

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons and fermions. Connections with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2 S +1) theory are found. Next, we proceed to derive the equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac 4-spinors. Due to serious problems with the interpretation of results we generalize the standard procedure and we obtain the spin-2 relativistic equations, which are consistent with the Einstein-Hilbert equation. We introduce the dual analogues of the Riemann tensor and we derive corresponding dynamical equations in the Minkowski space. Connections with the Marques-Spehler chiral gravity theory are discussed. The importance of the 4-vector field (and its gauge part) is pointed out. The spin-3/2 case is briefly discussed too.

scholarly journals A CFT distance conjecture

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Eric Perlmutter ◽  
Leonardo Rastelli ◽  
Cumrun Vafa ◽  
Irene Valenzuela
Keyword(s):  
Spin Symmetry ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Higher Spin ◽  
Spin Fields ◽  
Local Operators ◽  
Conformal Manifolds

Abstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

POINT PARTICLE–SYMMETRIC TENSORS INTERACTION AND GENERALIZED GAUGE PRINCIPLE

2003 ◽  
Vol 18 (27) ◽  
pp. 5021-5038 ◽  
Author(s):  
ARKADY Y. SEGAL
Keyword(s):  
Symmetric Tensor ◽  
Point Particle ◽  
Gauge Fields ◽  
Symmetric Tensors ◽  
Tensor Fields ◽  
First Order ◽  
Higher Spin ◽  
Infinite Collection ◽  
Higher Rank ◽  
Particle Action

The model of a point particle in the background of external symmetric tensor fields is analyzed from the higher spin theory perspective. It is proposed that the gauge transformations of the infinite collection of symmetric tensor fields may be read off from the covariance properties of the point particle action w.r.t. general canonical transformations. The gauge group turns out to be a semidirect product of all phase space canonical transformations to an Abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. A general configuration of external fields includes rank-0,1,2 symmetric tensors, so the whole system may be truncated to ordinary particle in Einstein–Maxwell backgrounds by switching off the higher-rank symmetric tensors. When otherwise all the higher rank tensors are switched on, the full gauge group provides a huge gauge symmetry acting on the whole infinite collection of symmetric tensors. We analyze this gauge symmetry and show that the symmetric tensors which couple to the point particle should not be interpreted as Fronsdal gauge fields, but rather as gauge fields of some conformal higher spin theories. It is shown that the Fronsdal fields system possesses twice as many symmetric tensor fields as is contained in the general background of the point particle. Besides, the particle action in general backgrounds is shown to reproduce De Wit–Freedman point particle–symmetric tensors first order interaction suggested many years ago, and extends their result to all orders in interaction, while the generalized equivalence principle completes the first order covariance transformations found in their paper, in all orders.

scholarly journals BRST APPROACH TO LAGRANGIAN FORMULATION OF BOSONIC TOTALLY ANTISYMMETRIC TENSOR FIELDS IN CURVED SPACE

2009 ◽  
Vol 24 (06) ◽  
pp. 401-414 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
V. A. KRYKHTIN ◽  
L. L. RYSKINA
Keyword(s):  
Gauge Symmetry ◽  
Lagrangian Formulation ◽  
Field Theories ◽  
Tensor Fields ◽  
Gauge Invariant ◽  
Curved Space ◽  
Spin Field ◽  
Gauge Models ◽  
Higher Spin ◽  
Lagrangian Construction

We apply the BRST approach, previously developed for higher spin field theories, to gauge-invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models both in massless and massive cases and the order of reducibility grows with the value of the rank of the antisymmetric field. In both cases the Lagrangians contain the sets of auxiliary fields and possess more rich gauge symmetry in comparison with standard Lagrangian formulation for the antisymmetric fields. This serves as an additional demonstration of universality of the BRST approach for Lagrangian constructions in various field models.

scholarly journals Dirac's Footsteps and Supersymmetry

2004 ◽  
Vol 19 (supp01) ◽  
pp. 89-97 ◽  
Author(s):  
Pierre Ramond
Keyword(s):  
Dirac Equation ◽  
Light Cone ◽  
Theoretical Interpretation ◽  
Compact Structure ◽  
Four Dimensions ◽  
Yang Mills ◽  
Higher Spin ◽  
Spin Fields ◽  
Front Form ◽  
M Theory

One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N=4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset F4/SO(9). The divergences are proportional to the trace over a non-compact structure containing the compact form of F4. Its nature is still unknown, but it could show the way to M-theory.

scholarly journals A compendium of sphere path integrals

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Y.T. Albert Law
Keyword(s):  
Standard Procedure ◽  
Path Integrals ◽  
Symmetric Tensor ◽  
Arbitrary Spin ◽  
Tensor Fields ◽  
Arbitrary Integer ◽  
Integer Spin ◽  
Higher Spin ◽  
Detailed Derivation ◽  
Massless Fields

Abstract We study the manifestly covariant and local 1-loop path integrals on Sd+1 for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions d ≥ 2. After reviewing the cases of massless fields with spin s = 1, 2, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins s ≥ 1. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski’s phase for any integer spin s ≥ 2. The derivations for low-spin (s = 0, 1, 2) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.

scholarly journals Massless higher spin cubic vertices in flat four dimensional space

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
M. V. Khabarov ◽  
Yu. M. Zinoviev
Keyword(s):  
Cosmological Constant ◽  
Dimensional Space ◽  
Four Dimensions ◽  
Equal Footing ◽  
Higher Derivative ◽  
Higher Spin ◽  
Spin Fields ◽  
Higher Spin Fields ◽  
Taking Care

Abstract In this paper we construct a number of cubic interaction vertices for massless bosonic and fermionic higher spin fields in flat four dimensional space. First of all, we construct these cubic vertices in AdS4 space using a so-called Fradkin-Vasiliev approach, which works only for the non-zero cosmological constant. Then we consider a flat limit taking care on all the higher derivative terms which FV-approach generates. We restrict ourselves with the four dimensions because this allows us to use the frame-like multispinor formalism which greatly simplifies all calculations and provides a description for bosons and fermions on equal footing.

scholarly journals EXPLICIT N = 2 SUPERSYMMETRY FOR HIGHER-SPIN FIELDS IN D = 4 AdS SUPERSPACE

2002 ◽  
Vol 17 (09) ◽  
pp. 1207-1252 ◽  
Author(s):  
A. YU. SEGAL ◽  
A. G. SIBIRYAKOV
Keyword(s):  
Fibre Bundle ◽  
Equations Of Motion ◽  
Component Analysis ◽  
Joint Model ◽  
Harmonic Superspace ◽  
Auxiliary Component ◽  
Covariant Derivatives ◽  
Simple Rules ◽  
Higher Spin ◽  
Spin Fields

We develop two N = 2 superfield formulations of free equations of motion for the joint model of all D = 4 massless higher-superspin fields. The explicit Osp (2|4) supersymmetry is achieved without exploiting the harmonic superspace, and with adding no auxiliary component fields to those of N = 1 superfields. The formulations are developed in two different Osp (2|4) homogeneous superspaces which have a structure of a fibre bundle over the standard D = 4 AdS superspace, with dimensions (7|4) and (7|8). The N = 2 covariant derivatives in these spaces are expressed in terms of N = 1 ones which give simple rules for component analysis.

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