Doubled geometry and T-folds

The doubled formulation of string theory, which is T-duality covariant andenlarges spacetime with extra coordinates conjugate to winding number, isreformulated and its geometric and topological features examined. It is used toformulate string theory in T-fold backgrounds with T-duality transitionfunctions and a quantum implementation of the constraints of the doubledformalism is presented. This establishes the quantum equivalence to the usualsigma-model formalism for world-sheets of arbitrary genus, provided atopological term is added to the action. The quantisation involves a localchoice of polarisation, but the results are independent of this. The naturaldilaton of the doubled formalism is duality-invariant and so T-duality is aperturbative symmetry for the perturbation theory in the corresponding couplingconstant. It is shown how this dilaton is related to the dilaton of theconventional sigma-model which does transform under T-duality. Thegeneralisation of the doubled formalism to the superstring is given and shownto be equivalent to the usual formulation. Finally, the formalism isgeneralised to one in which the whole spacetime is doubled.Comment: 35 pages. Minor correction