BNa–BLi solid-solution in A-site-vacant amphiboles: synthesis and cation ordering along the ferri-clinoferroholmquistite–riebeckite join.

Amphiboles were hydrothermally synthesized at 500 ∞C and 4 kbar in the system Li2O-Na2OFeO- Fe2O3-SiO2-H2O, with nominal compositions along the riebeckite [■Na2Fe3 2+ Fe2 3+Si8O22(OH)2]-ferri-clinoferroholmquistite [■Li2Fe3 2+Fe2 3+Si8O22(OH)2] join, where the exchange vector is NaLi–1 at the B-site. Experimental products were characterized by powder XRD and SEM-EDAX, confirming very high amphibole yield along the join (>95%, plus minor quartz). The XRD patterns can be indexed in C2/m, and the refined cell parameters show linear variation as a function of composition. For the BLi end-member, the IR spectrum shows a single sharp main band centered at 3614 cm–1, which is assigned to the FeFeFe-OH-A■ configuration. With increasing BNa in the mineral, this band broadens and shifts 4 cm–1 to higher frequencies. This effect can be attributed to the change in M4 site occupancy. Minor ANa (partial solid-solution toward arfvedsonite) is also observed with increasing sodium in the system. Mössbauer spectroscopy confirms the cation distribution provided by IR data, and shows that a small, but significant amount of Fe2+ occurs at M4 along the join. Infrared spectroscopy shows that the Li end-member has a very ordered structure, whereas intermediate compositions show local heterogeneities associated with the presence of two different B sites occupied by Na or Li

Inflationary de Sitter solutions from superstrings

In the framework of superstring compactifications with N=1 supersymmetry spontaneously broken, (by either geometrical fluxes, branes or else), we show the existence of new inflationary solutions. The time-trajectory of the scale factor of the metric a, the supersymmetry breaking scale m=m(Phi) and the temperature T are such that am and aT remain constant. These solutions request the presence of special moduli-fields: i) The universal "no-scale-modulus" Phi, which appears in all N=1 effective supergravity theories and defines the supersymmetry breaking scale m(Phi). ii) The modulus Phi_s, which appears in a very large class of string compactifications and has a Phi-dependent kinetic term. During the time evolution, a^4 rho_s remains constant as well, (rho_s being the energy density induced by the motion of Phi_s). The cosmological term Lambda(am), the curvature term k(am, aT) and the radiation term c_R=a^4 rho are dynamically generated in a controllable way by radiative and temperature corrections; they are effectively constant during the time evolution. Depending on Lambda, k and c_R, either a first or second order phase transition can occur in the cosmological scenario. In the first case, an instantonic Euclidean solution exists and connects via tunneling the inflationary evolution to another cosmological branch. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. In the second case, the big bang and the inflationary phase are smoothly connected.Comment: 37 pages, 4 eps figure

Soft Supersymmetry Breaking in Calabi-Yau Orientifolds with D-branes and Fluxes

In this paper we compute the N=1 effective low energy action for a stack of N space-time filling D3-branes in generic type IIB Calabi-Yau orientifolds with non-trivial background fluxes by reducing the Dirac-Born-Infeld and Chern-Simons actions. Specifically, we determine the Kahler potential for the excitations of the D-brane including their couplings to all bulk moduli fields. In the effective theory, N=1 supergravity is spontaneously broken by the presence of fluxes and we compute the induced soft supersymmetry breaking terms. We find an interesting structure in the resulting soft terms with generically universal soft scalar masses.Comment: LaTeX, 41 pages, minor corrections and references adde

General N = 1 Supersymmetric Fluxes in Massive Type IIA String Theory

We study conditions on general fluxes of massive Type IIA supergravity that lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these conditions in the case of SU(3)- as well as SU(2)-structures. SU(3)-structures imply that the internal space is constrained to be a nearly K\"ahler manifold with all the turned on fluxes, and the negative cosmological constant proportional to the mass parameter, and the dilaton fixed by the quantized ratio of the three-form and four-form fluxes. We further discuss the implications of such flux vacua with added intersecting D6-branes, leading to the chiral non-Abelian gauge sectors (without orientifold projections). Examples that break SU(3)-structures to SU(2)-ones allow for the internal space conformally flat (up to orbifold and orientifold projections), for which we give an explicit example. These results provide a starting point for further study of the four-dimensional (chiral) N = 1 supersymmetric solutions of massive Type IIA supergravity with D-branes and fluxes, compactified on orientifolds.Comment: 37 pages; changed the resulting gauge group on intersecting 6-branes, corrected the explicit example (with conformal flat internal space) as well as minor modifications and add a re

The effective action of N=1 Calabi-Yau orientifolds

We determine the N=1 low energy effective action for compactifications of type IIB string theory on compact Calabi-Yau orientifolds in the presence of background fluxes from a Kaluza-Klein reduction. The analysis is performed for Calabi-Yau threefolds which admit an isometric and holomorphic involution. We explicitly compute the Kahler potential, the superpotential and the gauge kinetic functions and check the consistency with N=1 supergravity. We find a new class of no-scale Kahler potentials and show that their structure can be best understood in terms of a dual formulation where some of the chiral multiplets are replaced by linear multiplets. For O3- and O7-planes the scalar potential is expressed in terms of a superpotential while for O5- and O9-planes also a D-term and a massive linear multiplet can be present. The relation with the associated F-theory compactifications is briefly discussed.Comment: 40 pages, typos corrected, discussion of no-scale property improve

Scalar geometry and masses in Calabi-Yau string models

We study the geometry of the scalar manifolds emerging in the no-scale sector of Kahler moduli and matter fields in generic Calabi-Yau string compactifications, and describe its implications on scalar masses. We consider both heterotic and orientifold models and compare their characteristics. We start from a general formula for the Kahler potential as a function of the topological compactification data and study the structure of the curvature tensor. We then determine the conditions for the space to be symmetric and show that whenever this is the case the heterotic and the orientifold models give the same scalar manifold. We finally study the structure of scalar masses in this type of geometries, assuming that a generic superpotential triggers spontaneous supersymmetry breaking. We show in particular that their behavior crucially depends on the parameters controlling the departure of the geometry from the coset situation. We first investigate the average sGoldstino mass in the hidden sector and its sign, and study the implications on vacuum metastability and the mass of the lightest scalar. We next examine the soft scalar masses in the visible sector and their flavor structure, and study the possibility of realizing a mild form of sequestering relying on a global symmetry.Comment: 36 pages, no figure

Hierarchically Split Supersymmetry with Fayet-Iliopoulos D-terms in String Theory

We show that in string theory or supergravity with supersymmetry breaking through combined F-terms and Fayet-Iliopoulos D-terms, the masses for charged scalars and fermions can be hierarchically split. The mass scale for the gauginos and higgsinos of the MSSM is controlled by the gravitino mass m_{3/2}, as usual, while the scalars get extra contributions from the D-terms of extra abelian U(1) factors, which can make them much heavier. The vanishing of the vacuum energy requires that their masses lie below {m_{3/2} M_{Pl}}^{1/2}, which for m_{3/2}=O(TeV) sets a bound of 10^{10-13} GeV. Thus, scalars with non-vanishing U(1) charges typically become heavy, while others remain light, producing a spectrum of scalars with masses proportional to their charges, and therefore non-universal. This is a modification of the split supersymmetry scenario, but with a light gravitino. We discuss how Fayet-Iliopoulos terms of this size can arise in orientifold string compactifications with D-branes. Furthermore, within the frame work of D-term inflation, the same vacuum energy that generates the heavy scalar masses can be responsible for driving cosmological inflation.Comment: 25 pages, 1 figure; v2: references adde

Towards Minkowski Vacua in Type II String Compactifications

We study the vacuum structure of compactifications of type II string theories on orientifolds with SU(3)xSU(3) structure. We argue that generalised geometry enables us to treat these non-geometric compactifications using a supergravity analysis in a way very similar to geometric compactifications. We find supersymmetric Minkowski vacua with all the moduli stabilised at weak string coupling and all the tadpole conditions satisfied. Generically the value of the moduli fields in the vacuum is parametrically controlled and can be taken to arbitrarily large values.Comment: 33 pages; v2 minor corrections, references added, version to appear in JHE