### Resumen

Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_{2}-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in (arXiv: 1505.04957) as an off-shell formulation of the minimal bosonic fourdimensional higher spin gravity theory. If F is unital and the Z_{2}-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H⊗. We give a new model of this type based on a twisting of C[Z_{2} ×Z_{4}], which leads to selfdual complexified gauge fields on AdS_{4}. If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z_{2})^{3}] that yields the original model, and the Clifford algebra Cℓ^{2n} which provides an FCS formulation of the bosonic Konstein-Vasiliev model with gauge algebra hu(4^{n-1}, 0) .

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

Número de artículo | 055401 |

Publicación | Journal of Physics A: Mathematical and Theoretical |

Volumen | 50 |

N.º | 5 |

DOI | |

Estado | Published - 4 ene 2017 |

### Huella dactilar

### ASJC Scopus subject areas

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

### Citar esto

*Journal of Physics A: Mathematical and Theoretical*,

*50*(5), [055401]. https://doi.org/10.1088/1751-8121/50/5/055401

}

*Journal of Physics A: Mathematical and Theoretical*, vol. 50, n.º 5, 055401. https://doi.org/10.1088/1751-8121/50/5/055401

**Frobenius-Chern-Simons gauge theory.** / Bonezzi, Roberto; Boulanger, Nicolas; Sezgin, Ergin; Sundell, Per.

Resultado de la investigación: Article

TY - JOUR

T1 - Frobenius-Chern-Simons gauge theory

AU - Bonezzi, Roberto

AU - Boulanger, Nicolas

AU - Sezgin, Ergin

AU - Sundell, Per

PY - 2017/1/4

Y1 - 2017/1/4

N2 - Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in (arXiv: 1505.04957) as an off-shell formulation of the minimal bosonic fourdimensional higher spin gravity theory. If F is unital and the Z2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H⊗. We give a new model of this type based on a twisting of C[Z2 ×Z4], which leads to selfdual complexified gauge fields on AdS4. If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z2)3] that yields the original model, and the Clifford algebra Cℓ2n which provides an FCS formulation of the bosonic Konstein-Vasiliev model with gauge algebra hu(4n-1, 0) .

AB - Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in (arXiv: 1505.04957) as an off-shell formulation of the minimal bosonic fourdimensional higher spin gravity theory. If F is unital and the Z2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H⊗. We give a new model of this type based on a twisting of C[Z2 ×Z4], which leads to selfdual complexified gauge fields on AdS4. If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z2)3] that yields the original model, and the Clifford algebra Cℓ2n which provides an FCS formulation of the bosonic Konstein-Vasiliev model with gauge algebra hu(4n-1, 0) .

KW - gauge theories

KW - higher-spin gravity

KW - topological field theory

UR - http://www.scopus.com/inward/record.url?scp=85010053518&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/50/5/055401

DO - 10.1088/1751-8121/50/5/055401

M3 - Article

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 5

M1 - 055401

ER -