scholarly journals Spin projection operators and higher-spin Cotton tensors in three dimensions

2019 ◽  
Vol 790 ◽  
pp. 389-395 ◽  
Author(s):  
Evgeny I. Buchbinder ◽  
Sergei M. Kuzenko ◽  
James La Fontaine ◽  
Michael Ponds
Keyword(s):  
Three Dimensions ◽  
Spin Projection ◽  
Projection Operators ◽  
Higher Spin

scholarly journals AdS (super)projectors in three dimensions and partial masslessness

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Daniel Hutchings ◽  
Sergei M. Kuzenko ◽  
Michael Ponds
Keyword(s):  
Isometry Group ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Irreducible Representations ◽  
Projection Operators ◽  
De Sitter ◽  
Arbitrary Integer ◽  
Higher Spin ◽  
Casimir Operators ◽  
Massless Fields

Abstract We derive the transverse projection operators for fields with arbitrary integer and half-integer spin on three-dimensional anti-de Sitter space, AdS3. The projectors are constructed in terms of the quadratic Casimir operators of the isometry group SO(2, 2) of AdS3. Their poles are demonstrated to correspond to (partially) massless fields. As an application, we make use of the projectors to recast the conformal and topologically massive higher-spin actions in AdS3 into a manifestly gauge-invariant and factorised form. We also propose operators which isolate the component of a field that is transverse and carries a definite helicity. Such fields correspond to irreducible representations of SO(2, 2). Our results are then extended to the case of $$ \mathcal{N} $$ N = 1 AdS3 supersymmetry.

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

scholarly journals Extending the spin projection operators for gravity models with parity-breaking in 3-D

2010 ◽  
Vol 374 (34) ◽  
pp. 3410-3415 ◽  
Author(s):  
C.A. Hernaski ◽  
B. Pereira-Dias ◽  
A.A. Vargas-Paredes
Keyword(s):  
Gravity Models ◽  
Spin Projection ◽  
Projection Operators ◽  
Parity Breaking

scholarly journals An action for matter coupled higher spin gravity in three dimensions

2016 ◽  
Vol 2016 (5) ◽  
Author(s):  
Roberto Bonezzi ◽  
Nicolas Boulanger ◽  
Ergin Sezgin ◽  
Per Sundell
Keyword(s):  
Higher Spin Gravity ◽  
Three Dimensions ◽  
Higher Spin

scholarly journals Unitarity of Singh-Hagen Model in D Dimensions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Elias L. Mendonça ◽  
R. Schimidt Bittencourt
Keyword(s):  
General Expression ◽  
Spin Projection ◽  
Projection Operators ◽  
Source Terms ◽  
Particle Content ◽  
Complete Set

The particle content of the Singh-Hagen model (SH) in D dimensions is revisited. We suggest a complete set of spin-projection operators acting on totally symmetric rank-3 fields. We give a general expression for the propagator and determine the coefficients of the SH model confirming previous results of the literature. Adding source terms, we provide a unitarity analysis in D dimensions. In addition, we have also analyzed the positivity of the massless Hamiltonian.

scholarly journals Higher derivative fermionic field equation in the first-orderformalism

2007 ◽  
Vol 85 (8) ◽  
pp. 887-897 ◽  
Author(s):  
S I Kruglov
Keyword(s):  
Dirac Equation ◽  
Spin Projection ◽  
Electromagnetic Current ◽  
Pure Spin ◽  
Projection Operators ◽  
Third Order ◽  
First Order ◽  
Generalized Dirac Equation ◽  
Electromagnetic Interactions ◽  
Higher Derivative

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first-order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found that extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and nonminimal(anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first-order equation is obtained.PACS Nos.: 03.65.Pm, 11.10.Ef; 12.10.Kt

scholarly journals Higher spin black hole entropy in three dimensions

2013 ◽  
Vol 2013 (4) ◽  
Author(s):  
Alfredo Pérez ◽  
David Tempo ◽  
Ricardo Troncoso
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Three Dimensions ◽  
Higher Spin

scholarly journals The action for higher spin black holes in three dimensions

2012 ◽  
Vol 2012 (7) ◽  
Author(s):  
Máximo Bañados ◽  
Rodrigo Canto ◽  
Stefan Theisen
Keyword(s):  
Black Holes ◽  
Three Dimensions ◽  
Higher Spin

CONFORMAL SUPERALGEBRAS OF HIGHER SPINS

1989 ◽  
Vol 04 (24) ◽  
pp. 2363-2375 ◽  
Author(s):  
E.S. FRADKIN ◽  
V. Ya. LINETSKY
Keyword(s):  
Explicit Expression ◽  
Effective Action ◽  
Three Dimensions ◽  
Four Dimensions ◽  
Infinite Dimensional ◽  
Higher Spin ◽  
Higher Spins ◽  
Conformal Superalgebras

Infinite-dimensional conformal higher spin superalgebras are constructed. Based on the superalgebra in three dimensions, an explicit expression for the effective action is found. In four dimensions, the curvatures of higher spin conformal superalgebras are obtained.

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