Doubled Geometry and T-Folds

TL;DR

This paper reformulates the doubled string theory approach, explores its geometric features, and demonstrates its quantum equivalence to traditional models, enabling T-duality covariant descriptions including T-fold backgrounds and spacetime doubling.

Contribution

It introduces a quantum formulation of doubled string theory with T-fold backgrounds, establishing equivalence to standard models and extending to superstrings and spacetime doubling.

Findings

Quantum equivalence to sigma-models established

T-duality invariant dilaton identified

Formalism extended to superstring and spacetime doubling

Abstract

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate string theory in T-fold backgrounds with T-duality transition functions and a quantum implementation of the constraints of the doubled formalism is presented. This establishes the quantum equivalence to the usual sigma-model formalism for world-sheets of arbitrary genus, provided a topological term is added to the action. The quantisation involves a local choice of polarisation, but the results are independent of this. The natural dilaton of the doubled formalism is duality-invariant and so T-duality is a perturbative symmetry for the perturbation theory in the corresponding coupling constant. It is shown how this dilaton is related to the dilaton of the conventional sigma-model which does transform under T-duality. The generalisation of the doubled formalism to the superstring is given and shown to be equivalent to the usual formulation. Finally, the formalism is generalised to one in which the whole spacetime is doubled.