A new spacetime symmetry

Date: 2015-10-07; view: 747.

Supersymmetry essentials

Supersymmetry is an extension of the known spacetime symmetries [3]. The spacetime symmetries of rotations, boosts, and translations are generated by angular momentum operators L_i, boost operators K_i, and momentum operators P_μ, respectively. The L and K generators form Lorentz symmetry, and all 10 generators together form Poincare symmetry. Supersymmetry is the symmetry that results when these 10 generators are further supplemented by fermionic operators Q_α. It emerges naturally in string theory and, in a sense that may be made precise [4], is the maximal possible extension of Poincare symmetry.

If a symmetry exists in nature, acting on a physical state with any generator of the symmetry gives another physical state. For example, acting on an electron with a momentum operator produces another physical state, namely, an electron translated in space or time. Spacetime symmetries leave the quantum numbers of the state invariant—in this example, the initial and final states have the same mass, electric charge, etc.

In an exactly supersymmetric world, then, acting on any physical state with the supersymmetry generator Q_α produces another physical state. As with the other spacetime generators, Q_α does not change the mass, electric charge, and other quantum numbers of the physical state. In contrast to the Poincare generators, however, a supersymmetric transformation changes bosons to fermions and vice versa. The basic prediction of supersymmetry is, then, that for every known particle there is another particle, its superpartner, with spin differing by 1/2.

One may show that no particle of the standard model is the superpartner of another. Supersymmetry therefore predicts a plethora of superpartners, none of which has been discovered. Mass degenerate superpartners cannot exist—they would have been discovered long ago—and so supersymmetry cannot be an exact symmetry. The only viable supersymmetric theories are therefore those with non-degenerate superpartners. This may be achieved by introducing supersymmetry-breaking contributions to superpartner masses to lift them beyond current search limits. At first sight, this would appear to be a drastic step that considerably detracts from the appeal of supersymmetry. It turns out, however, that the main virtues of supersymmetry are preserved even if such mass terms are introduced. In addition, the possibility of supersymmetric dark matter emerges naturally and beautifully in theories with broken supersymmetry.