1306.1247 (Pedro D. Alvarez et al.)

Local supersymmetry without SUSY partners    [PDF]

Pedro D. Alvarez, Pablo Pais, Jorge Zanelli

A gauge theory for a superalgebra that could describe the low energy particle phenomenology is constructed. The system includes an internal gauge connection one-form A, a spin-1/2 Dirac fermion \psi in the fundamental representation of the internal symmetry group, and a Lorentz connection \omega^{ab}. The important distinctive features between this theory and standard supersymmetries are: i) the number of fermionic and bosonic states are not necessarily equal; ii) no superpartners appear, "bosoninos" or s-leptons commonly found in standard supersymmetry theories are absent; iii) although the supersymmetry is local and gravity is included, there is no gravitino; iv) fermions get mass from their coupling to the background or from a higher order self-coupling, while bosons remain massless. In odd dimensions, the Chern-Simons action is fully invariant under the entire local superalgebra. In even dimensions, the Yang-Mills form L=\kappa is the only natural option and the symmetry breaks down to [(Internal Gauge) times (Lorentz)]. In four dimensions, following the Townsend-MacDowell-Mansouri construction out of a osp(4|2) ~ usp(2,2|1) connection produces a Lagrangian invariant under the subalgebra [u(1) + so(3,1)], where the only non-standard additional piece is the Nambu-Jona Lasinio term. In this case, the Lagrangian depends on a single dimensionful parameter that sets the values of Newton's constant, the cosmological constant and the NJL coupling.

View original: http://arxiv.org/abs/1306.1247