Global aspects of T-duality, gauged sigma models and T-folds

Abstract

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to Tduality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

Toroidal orientifolds in IIA with general NS-NS fluxes

“…We still, however, need to satisfy the tadpole constraint. Indeed, since [δ O6 ] = 4b 1 , we find 41) where N 1 and N 2 are the number of D-branes wrapping the cycle dual to b 1 or b 2 respectively. Actually one needs to be a bit careful here; a supersymmetric D-brane should have a positive volume as calibrated by Re Ω, but for the cycle dual to b 2 the orientation picked out by this condition depends on whether U is less than or greater than one half.…”

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

“…It is instructive to investigate the action of T-duality in connection with geometric and non-geometric fluxes (see also the discussion in [82][83][84]). Let us consider again the stringy compactification on a T-fold locally described by a space T d × S 1 with monodromy twist M ∈ O(d, d; Z).…”

“…The shift in X is accompanied a purely left-moving Z 4 rotation of the fiber, whereas the shift inX is accompanied by a Z 2 rotation of the right-movers: Here, the circle coordinate X and its dualX should be thought of as linear combinations of X L and X R . Since the perturbation depends on the left-and right-moving circle coordinates only through exponential functions, the corresponding operators O q L ,q R ∼ e iq L X L +iq R X R carry well-defined conformal weight and the deformation can be consistently defined at the string level, for any circle radius R. It would be interesting to obtain an analogous formulation of this deformation in terms of a double σ-model, along the lines of [84,109,110].…”

Einstein Supergravity and New Twistor String Theories

“…Then the gauged theory is well-defined provided the gauge fieldsB i are taken to be connections on the pull-back ofX to a bundle over the world-sheet, by a similar construction to that given in [34]. The theory is locally the same as that described above.…”