Conformal non-geometric gravity in six dimensions andM-theory above the Planck energy

Abstract

The proposal that a strong-coupling limit of the five-dimensional type IIstring theory (M-theory compactified on a 6-torus) in which the Plancklength becomes infinite could give a six-dimensional superconformalphase of M-theory is reviewed. This limit exists for the free theory,giving a six-dimensional theory with (4,0) supersymmetry compactifiedon a circle whose radius gives the five-dimensional Planck length. Thefree six-dimensional theory has a fourth rank tensor gauge field with thesymmetries of the Riemann tensor instead of a symmetric tensor gaugefield, but its dimensional reduction gives conventional linearized gravityin five dimensions. The possibility of an interacting form of this theoryexisting and the consequences it would have for the geometric picture ofgravity are discussed.