  We argue that the fundamental Theory of Everything is a conventional field
theory defined in the flat multidimensional bulk. Our Universe should be
obtained as a 3-brane classical solution in this theory. The renormalizability
of the fundamental theory implies that it involves higher derivatives (HD). It
should be supersymmetric (otherwise one cannot get rid of the huge induced
cosmological term) and probably conformal (otherwise one can hardly cope with
the problem of ghosts) . We present arguments that in conformal HD theories the
ghosts (which are inherent for HD theories) might be not so malignant. In
particular, we present a nontrivial QM HD model where ghosts are absent and the
spectrum has a well defined ground state. The requirement of superconformal
invariance restricts the dimension of the bulk to be D < 7. We suggest that the
TOE lives in six dimensions and enjoys the maximum N = (2,0) superconformal
symmetry. Unfortunately, no renormalizable field theory with this symmetry is
presently known. We construct and discuss an N = (1,0) 6D supersymmetric gauge
theory with four derivatives in the action. This theory involves a
dimensionless coupling constant and is renormalizable. At the tree level, the
theory enjoys conformal symmetry, but the latter is broken by quantum anomaly.
The sign of the beta function corresponds to the Landau zero situation.
