Duality twists, orbifolds, and fluxes

Abstract

We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on the moduli space. For certain twists, this mechanism is equivalent to introducing internal fluxes but is more general and can be used to stabilize some of the moduli. We show that the potential has stable minima with zero energy precisely at the fixed points of the twist group. In string theory, when the twist belongs to the T-duality group, the theory at the minimum has an exact CFT description as an orbifold. We also discuss more general twists by nonperturbative Uduality transformations.

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

“…The results of [28] suggest that T-duality should generalise to this case, but the non-abelian structure leads to issues similar to those that arise in non-abelian duality [36], [37], [38], so that the approach used here appears difficult to implement in that case.…”

“…In [19] it was argued that in certain cases the T-dual is a T-fold -a space which looks locally like a manifold with g, H but where the transition functions between patches involve Tduality transformations. Examples of such non-geometric string backgrounds have been explored in [19], [27][28][29][30][31][32][33][34]. It will be shown here that the only condition for a T-duality to a T-fold to be possible is that the constants ι m ι n ι p H vanish, and no condition on ι m ι n H is needed.…”

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

“…These models [18,19,20,21,22,23,24], depending on the choice of fluxes, can give rise to no-scale supergravities [25] with partially broken supersymmetry or other type of vacua. These solutions can have either Minkowski or AdS geometry.…”

Non-geometric backgrounds based on topological interfaces

“…They are rather ubiquitous, and constitute key ingredients in understanding intrinsic nature of quantum strings, such as string vacua and dualities. Of particular interest among them are the backgrounds whose transition functions involve duality transformations [1][2][3]. Since the dualities relate different backgrounds, the notion of the Riemannian geometry is generally lost.…”