Abstract

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 includesa (non-) abeliangauge potential A, a spin-1/2 Dirac spinor psi, the Lorentz connection omega(ab), and the vielbein e(mu)(a). The connection one-form A is in the adjoint representation of G, while psi is in the fundamental. In contrast tostandard 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, SO(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 YangMills (YM) form is the only natural option and the symmetry breaks down to G circle times SO(1, D-1). In four dimensions, the construction follows the Townsend-Mac Dowell-Mansouri approach, starting with an osp(4 vertical bar 2) similar to usp(2,2 vertical bar 1) connection. Due to the absence of osp(4 vertical bar 2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under u(1) circle times 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. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license