Predictions of Lorentz-Violating Supergravity

By Roland Allen, Texas A&M University

Roland E. Allen and Seiichirou Yokoo

Lorentz invariance and supersymmetry are distinct symmetries, and it is possible to have either without the other [1]. In earlier work [2-5], a theory was proposed in which Lorentz invariance does not hold near the Planck scale, but instead emerges to become almost exact at much lower energies. The theory includes a form of supergravity with highly unconventional and experimentally testable predictions, which we will amplify in the present talk. For example, the sfermions are spin 1/2 bosons, and the gauginos are spin 1 fermions. In this talk we will explain in detail how particles with such unusual properties can be treated consistently in both path-integral and canonical quantization. (For the case of spin 1/2 bosons, see also Ref. 3.) We will discuss some other obvious issues with the present theory, including causality, the relevance of the spin-statistics and CPT theorems [6], and consistency with the experimental and observational tests of Lorentz invariance [5]. Most importantly, we will explore the experimental predictions of Lorentz-violating supergravity. For example, the equations of motion of the sparticles are quite different from those in standard SUSY, making the energy-momentum relations and distributions of products quite different. In addition, many of the processes featured in standard SUSY are forbidden in the present theory. [1] R. E. Allen, in the Concise Encyclopedia of Supersymmetry, edited by Jonathan Bagger, Steven Duplij, and Warren Siegel (Kluwer, 2003). [2] R.E. Allen, International Journal of Modern Physics A 12, 2385 (1997); hep-th/9612041. [3] R. E. Allen, in Beyond the Desert 2002, edited by H. V. Klapdor-Kleingrothaus (Institute of Physics, London, 2002); hep-th/0008032. [4] R. E. Allen, in Beyond the Desert 2003, edited by H. V. Klapdor-Kleingrothaus; hep-th/0310039. [5] R. E. Allen and S. Yokoo, in the proceedings of the Second International Conference on Particle and Fundamental Physics in Space, edited by R. Battiston (Nuclear Physics B suppl.); hep-th/ 0402154. [6] The spin-statistics connection is in a sense a rather fragile result that depends critically on Lorentz invariance: R. E. Allen and A. R. Mondragon, Physical Review A 68, 046101 (2003); quant-ph/ 0304088.