Current algebra formulation of M-theory based on E11 Kac–Moody algebra

Abstract

Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac–Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the [Formula: see text] Kac–Moody algebra that was shown recently[Formula: see text] to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside [Formula: see text], so that, by constructing the current algebra of [Formula: see text], I obtain both internal gauge theory and gravity theory. The energy–momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein–Hilbert action.