### Resumen

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 dS_{4}, 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 N = 2 supersymmetric higher spin theory in dS_{4}, on which we elaborate further, is included in this class of models. A subset of the Konstein-Vasiliev algebras are the minimal higher spin extensions of the AdS_{4} superalgebra with osp(4|N) with N = 1, 2, 4 mod 4, whose R-symmetry can be realized using fermionic oscillators. We tensor these algebras with appropriate internal symmetry algebras, namely u(n) for N = 2 mod 4 and so(n) or usp(n) for N = 1, 4 mod 4. We show that the N = 3 mod 4 higher spin algebras are isomorphic to those with N = 4 mod 4. We describe the fully nonlinear higher spin theories based on these algebras, including the coupling between the adjoint and twisted-adjoint master fields. We elaborate further on N = 6 the model in AdS_{4}, and provide two equivalent descriptions one of which exhibits manifestly its relation to the N = 8 model.

Idioma original | English |
---|---|

Número de artículo | 214022 |

Publicación | Journal of Physics A: Mathematical and Theoretical |

Volumen | 46 |

N.º | 21 |

DOI | |

Estado | Published - 31 may 2013 |

### Huella dactilar

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Citar esto

*Journal of Physics A: Mathematical and Theoretical*,

*46*(21), [214022]. https://doi.org/10.1088/1751-8113/46/21/214022

}

*Journal of Physics A: Mathematical and Theoretical*, vol. 46, n.º 21, 214022. https://doi.org/10.1088/1751-8113/46/21/214022

**Supersymmetric higher spin theories.** / Sezgin, Ergin; Sundell, Per.

Resultado de la investigación: Article

TY - JOUR

T1 - Supersymmetric higher spin theories

AU - Sezgin, Ergin

AU - Sundell, Per

PY - 2013/5/31

Y1 - 2013/5/31

N2 - 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 dS4, 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 N = 2 supersymmetric higher spin theory in dS4, on which we elaborate further, is included in this class of models. A subset of the Konstein-Vasiliev algebras are the minimal higher spin extensions of the AdS4 superalgebra with osp(4|N) with N = 1, 2, 4 mod 4, whose R-symmetry can be realized using fermionic oscillators. We tensor these algebras with appropriate internal symmetry algebras, namely u(n) for N = 2 mod 4 and so(n) or usp(n) for N = 1, 4 mod 4. We show that the N = 3 mod 4 higher spin algebras are isomorphic to those with N = 4 mod 4. We describe the fully nonlinear higher spin theories based on these algebras, including the coupling between the adjoint and twisted-adjoint master fields. We elaborate further on N = 6 the model in AdS4, and provide two equivalent descriptions one of which exhibits manifestly its relation to the N = 8 model.

AB - 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 dS4, 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 N = 2 supersymmetric higher spin theory in dS4, on which we elaborate further, is included in this class of models. A subset of the Konstein-Vasiliev algebras are the minimal higher spin extensions of the AdS4 superalgebra with osp(4|N) with N = 1, 2, 4 mod 4, whose R-symmetry can be realized using fermionic oscillators. We tensor these algebras with appropriate internal symmetry algebras, namely u(n) for N = 2 mod 4 and so(n) or usp(n) for N = 1, 4 mod 4. We show that the N = 3 mod 4 higher spin algebras are isomorphic to those with N = 4 mod 4. We describe the fully nonlinear higher spin theories based on these algebras, including the coupling between the adjoint and twisted-adjoint master fields. We elaborate further on N = 6 the model in AdS4, and provide two equivalent descriptions one of which exhibits manifestly its relation to the N = 8 model.

UR - http://www.scopus.com/inward/record.url?scp=84878117906&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/21/214022

DO - 10.1088/1751-8113/46/21/214022

M3 - Article

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 21

M1 - 214022

ER -