Is ToE a higher-derivative field theory?

by Smilga, A. (Université de Nantes)

Thursday 18 Jan 2007, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

We present the arguments that the Theory of Everything might be a conventional supersymmetric field theory in higher dimensions involving higher derivatives in the action. Out Universe should then be identified with a 3-brane classical solution in this theory. Gravity has the status of effective theory induced on the world-volume of this brane. Using the harmonic superspace technique, we construct and discuss the superconformal at the classical level higher-derivative gauge theory in six dimensions. This theory is renormalizable, with the sign of the beta function describing a Landau zero situation, like in ordinary QED. The theory involves chiral anomaly, but it is cancelled if adding a hypermultiplet to the gauge multiplet in the adjoint representation. The theory with the hypermultiplet involves, however, an infinite number of propagating fields. It is not clear at the moment how to handle them. Higher derivative theories usually are considered to be sick, because most of them involve ghosts associated with violation of unitarity. Studying different toy models, we show, however, that violation of unitarity is not a NECESSARY feature of higher derivative theories and there ARE ways to tame the ghosts. In particular, we show how to do it for the 5D superconformal gauge theory in the sector where the scalar v.e.v. is absent. We discuss also a bunch of quantum mechanical higher-derivative models (supersymmetric and not), which are rather amusing and might present interest by themselves.