Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T 6 /Z 4 .

The phase structure of flavoured N = 2 SYM on a three sphere in an external magnetic field is studied. The pairing effect of the magnetic field competes with the dissociating effect of the Casimir energy, leading to an interesting phase structure of confined and deconfined phases separated by a critical curve of a first order quantum phase transition. At vanishing magnetic field the phase transition is of a third order. For sufficiently strong magnetic field, the only stable phase is the confined phase and magnetic catalysis of chiral symmetry breaking is realized. The meson spectra of the theory exhibit Zeeman splitting and level crossing and feature a finite jump at the phase transition between the confined and deconfined phases. At strong magnetic field the ground state has a massless mode corresponding to the Goldstone boson associated with the spontaneously broken U (1) R-symmetry analogous to the η meson in QCD.

We apply the methods of DeWolfe et al. [hep-th/0505160] to a T 6 /Z 4 orientifold model. This is the first step in an attempt to build a phenomenologically interesting meta-stable de Sitter model with small cosmological constant and standard model gauge groups. Basic setupIn this section, we outline the properties of the type IIA orientifold model under investigation, namely an orientifolded T 6 /Z 4 orbifold that preserves N = 1 supersymmetry. A detailled discussion of this model can be found in [28].3 One can stabilize all the complex structure moduli but only one linear combination of the axions. 4 The T 6 /Z 4 orbifold is among those studied in [26,27] and has been shown to admit consistent string propagation, e.g., preserving modular invariance.5 The actions of Θ 1 , Θ 2 , Θ 3 all yield 16 fixed points. However, four pairs of elements, namely those involving combinations of Θ 0 = ½ and Θ 2 : (z 1 , z 2 , z 3 ) → (α 2 z 1 , α 2 z 2 , z 3 ), leave at least one of the T 2 factors invariant, thus not contributing to the sum, as χ(T 6 ) = χ(T 2 ) = 0.

We extend the analysis of hep-th/0408069 on a Lorentz invariant interpretation of noncommutative spacetime to field theories on non-anticommutative superspace with half the supersymmetries broken. By defining a Drinfeld-twisted Hopf superalgebra, it is shown that one can restore twisted supersymmetry and therefore obtain a twisted version of the chiral rings along with certain Ward-Takahashi identities. Moreover, we argue that the representation content of theories on the deformed superspace is identical to that of their undeformed cousins and comment on the consequences of our analysis concerning non-renormalization theorems.

The Seiberg-Witten limit of fermionic N=2 string theory with nonvanishing B-field is governed by noncommutative self-dual Yang-Mills theory (ncSDYM) in 2+2 dimensions. Conversely, the self-duality equations are contained in the equation of motion of N=2 string field theory in a B-field background. Therefore finding solutions to noncommutative self-dual Yang-Mills theory on R 2,2 might help to improve our understanding of nonperturbative properties of string (field) theory. In this paper, we construct nonlinear soliton-like and multi-plane wave solutions of the ncSDYM equations corresponding to certain D-brane configurations by employing a solution generating technique, an extension of the so-called dressing approach. The underlying Lax pair is discussed in two different gauges, the unitary and the hermitean gauge. Several examples and applications for both situations are considered, including abelian solutions constructed from GMSlike projectors, noncommutative U (2) soliton-like configurations and interacting plane waves. We display a correspondence to earlier work on string field theory and argue that the solutions found here can serve as a guideline in the search for nonperturbative solutions of nonpolynomial string field theory.