## Abstract

We present a gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz (so(1,D-1)) algebras. These two symmetries are connected by fermionic supercharges. The field content of the system includes a (non-)abelian gauge potential A, a spin-1/2 Dirac spinor ψ, the Lorentz connection ^{ωa b}, and the vielbein eμa. The connection one-form A is in the adjoint representation of G, while ψ is in the fundamental. In contrast to standard supersymmetry and supergravity, the metric is not a fundamental field and is in the center of the superalgebra: it is not only invariant under the internal gauge group, G, and under Lorentz transformations, S O(1, D - 1), but is also invariant under supersymmetry.The distinctive features of this theory that mark the difference with standard supersymmetries are: i) the number of fermionic and bosonic states is not necessarily the same; ii) there are no superpartners with equal mass; iii) although this supersymmetry originates in a local gauge theory and gravity is included, there is no gravitino; iv) fermions acquire mass from their coupling to the background or from higher order self-couplings, while bosons remain massless. In odd dimensions, the Chern-Simons (CS) form provides an action that is (quasi-)invariant under the entire superalgebra. In even dimensions, the Yang-Mills (YM) form is the only natural option and the symmetry breaks down to G ⊗ S O(1, D - 1). In four dimensions, the construction follows the Townsend-Mac Dowell-Mansouri approach, starting with an osp(4|2)~usp(2,2|1) connection. Due to the absence of o s p(4|. 2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under u(1)⊕so(3,1), which includes a Nambu-Jona-Lasinio (NJL) term. In this case, the Lagrangian depends on a single dimensionful parameter that fixes Newton's constant, the cosmological constant and the NJL coupling.

Original language | English |
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Pages (from-to) | 314-321 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 735 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

### Bibliographical note

Funding Information:Enlightening discussions with A. Balachandran, N. Boulanger, F. Canfora, G. Catren, R.M. Fernandes, G. Giribet, M. Hassaïne, J. Helayel-Neto, A. Iorio, M. Loewe, V.P. Nair, H. Nicolai, D. Ponomarev, E. Rodríguez, K. Siampos, P. Sundell, P.K. Townsend, R. Troncoso, and M. Valenzuela are warmly acknowledged. We also thank A. Chamseddine for bringing to our attention Refs. [8] . P.P. thanks the Physique Théorique et Mathématique group of the Université Libre de Bruxelles, the International Solvay Institutes and the Faculty of Mathematics and Physics of Charles University in Prague for the kind hospitality during the development of this work, which was partially funded through a travel grant from Universidad Andrés Bello's Vicerrectoría de Investigación y Doctorado . This work was supported by FONDECYT -Chile grant 1140155 and Becas Chile 74130061 . The Centro de Estudios Científicos (CECS) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of CONICYT -Chile.

## ASJC Scopus subject areas

- Nuclear and High Energy Physics