Generalised space–time and duality

In this Letter we consider the previously proposed generalised space–time and investigate the structure of the field theory upon which it is based. In particular, we derive a SO(D,D)SO(D,D) formulation of the bosonic string as a non-linear realisation at lowest levels of E11⊗sl1E11⊗sl1 where l1l1 is the first fundamental representation. We give a Hamiltonian formulation of this theory and carry out its quantisation. We argue that the choice of representation of the quantum theory breaks the manifest SO(D,D)SO(D,D) symmetry but that the symmetry is manifest in a non-commutative field theory. We discuss the implications for the conjectured E11E11 symmetry and the role of the l1l1 representation.