In this paper we consider a class of exactly solvable closed string flux backgrounds that exhibit non-commutativity in the closed string coordinates. They are realized in terms of freely-acting asymmetric Z N -orbifolds, which are themselves close relatives of twisted torus fibrations with elliptic Z N -monodromy (elliptic T-folds). We explicitly construct the modular invariant partition function of the models and derive the non-commutative algebra in the string coordinates, which is exact to all orders in α ′ . Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz backgrounds and nongeometric fluxes.

We compute instantonic effects in globally consistent T 6 /Z 2 × Z 2 orientifold models with discrete torsion and magnetised D-branes. We consider fractional branes and instantons wrapping the same rigid cycles. We clarify and analyse in detail the lowenergy effective action on D-branes in these models. We provide explicit examples where instantons induce linear terms in the charged fields, or non-perturbative mass terms are generated. We also find examples where the gauge theory on fractional branes has conformal symmetry at one-loop, broken by instantonic mass terms at a hierarchically small energy scale.

Abstract:We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes. Exploiting the connection between internal fluxes and structure constants of the gaugings in the reduced supergravity theory, we can identify the types of fluxes arising in certain classes of freely-acting symmetric and asymmetric orbifolds. We give a general procedure for deriving the gauge algebra of the effective gauged supergravity using the exact CFT description at the orbifold point. We find that the asymmetry is, in general, related to the presence of non-geometric Q-and R-fluxes. The action of T-duality is studied explicitly on various orbifold models and the resulting transformation of the fluxes is derived. Several explicit examples are provided, including compactifications with geometric fluxes, Q-backgrounds (T-folds) and R-backgrounds. In particular, we present an asymmetric Z 4 × Z 2 orbifold in which all geometric and nongeometric fluxes ω, H, Q, R are turned on simultaneously. We also derive the corresponding flux backgrounds, which are not in general T-dual to geometric ones, and may even simultaneously depend non-trivially on both the coordinates and their winding T-duals.

We show how the brane wrapping rules, recently discovered in closed oriented string theories compactified on tori, are extended to the case of the Type IIA string compactified on K3. To this aim, a crucial role is played by the duality between this theory and the Heterotic string compactified on a four-dimensional torus T 4 . We first show how the wrapping rules are applied to the T 4 /Z N orbifold limits of K3 by relating the D0 branes, obtained as D2 branes wrapping two-cycles, to the perturbative BPS states of the Heterotic theory on T 4 . The wrapping rules are then extended to the solitonic branes of the Type IIA string, finding agreement with the analogous Heterotic states. Finally, the geometric Type IIA orbifolds are mapped, via T-duality, to non-geometric Type IIB orbifolds, where the wrapping rules are also at work and consistent with string dualities.

We study a class of compactifications of M-theory to three dimensions that preserve N = 2 supersymmetry and which have the defining feature that a probe space-time filling M2 brane feels a non-trivial potential on the internal manifold. Using M-theory/Ftheory duality such compactifications include the uplifts of 4-dimensional N = 1 type IIB compactifications with D3 potentials to strong coupling. We study the most general 8-dimensional manifolds supporting these properties, derive the most general flux that induces an M2 potential, and show that it is parameterised in terms of two real vectors. We study the supersymmetry equations when only this flux is present and show that over the locus where the M2 potential is non-vanishing the background takes the form of a Calabi-Yau three-fold fibered over a 2-dimensional base spanned by the flux vectors, while at the minima of the potential the flux vanishes. Allowing also for non-vanishing fourform flux with one leg in the internal directions we find that the Calabi-Yau three-fold in the fibration is replaced by an SU(3)-structure manifold with torsion classes satisfying 2W 4 = −W 5 .

We elaborate on a recently discovered phenomenon where a scalar field close to big-bang is forced to climb a steep potential by its dynamics. We analyze the phenomenon in more general terms by writing the leading order equations of motion near the singularity. We formulate the conditions for climbing to exist in the case of several scalars and after inclusion of higher-derivative corrections and we apply our results to some models of moduli stabilization. We analyze an example with steep stabilizing potential and notice again a related critical behavior: for a potential steepness above a critical value, going backwards towards big-bang, the scalar undergoes wilder oscillations, with the steep potential pushing it back at every passage and not allowing the scalar to escape to infinity.Whereas it was pointed out earlier that there are possible implications of the climbing phase to CMB, we point out here another potential application, to the issue of initial conditions in inflation.

Abstract:We analyze the action of the target-space modular group in toroidal type IIB orientifold compactifications with magnetized D-branes and continuous Wilson lines. The transformation of matter fields agree with that of twisted fields in heterotic compactifications, constituting a check of type I/heterotic duality. We identify the holomorphic N = 1 variables for these compactifications. Matter fields and closed string moduli are both redefined by open string moduli. The redefinition of matter fields can be read directly from the perturbative Yukawa couplings, whereas closed string moduli redefinitions are obtained from D-brane instanton superpotential couplings. The resulting expressions reproduce and generalize, in the presence of internal magnetic fields, previous results in the literature.

Abstract:We analyze the process of string vacuum destabilization due to instanton induced superpotential couplings which depend linearly on charged fields. These nonperturbative instabilities result in potentials for the D-brane moduli and lead to processes of D-brane recombination, motion and partial moduli stabilization at the non-perturbative vacuum. By using techniques of D-brane instanton calculus, we explicitly compute this scalar potential in toroidal orbifold compactifications with magnetized D-branes by summing over the possible discrete instanton configurations. We illustrate explicitly the resulting dynamics in globally consistent models. These instabilities can have phenomenological applications to breaking hidden sector gauge groups, open string moduli stabilization and supersymmetry breaking. Our results suggest that breaking supersymmetry by Polonyi-like models in string theory is more difficult than expected.