Some aspects of string compactifications with non-geometric fluxes are revisited in the light of recent progress in double field theory. After rederiving the general form of these fluxes, we consider the proposed flux induced four-dimensional effective superpotential and oxidize its induced scalar potential to terms in a ten-dimensional action. This analysis is performed independently for an explicit toroidal type IIA and its T-dual type IIB orientifold. We show in detail that the result of this bottom-up approach is compatible with the gauged supergravity motivated flux formulation of the double field theory action in both the NS-NS and the R-R sector.

We address issues related to (i) a proposal for resolving a long-standing tension between large volume cosmology and phenomenology as regards reconciliation of requirements of different gravitino masses within the same string-theoretic framework, as well as (ii) evaluation of soft supersymmetry breaking terms and open-string moduli masses in the context of type IIB large volume compactifications involving orientifolds of the Swiss-Cheese Calabi-Yau WCP 4 [1, 1, 1, 6, 9] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the "big" divisor Σ B as well as supporting D7-brane fluxes. In addition, we also include perturbative α ′ -corrections and non-perturbative world-sheet instanton corrections to the Kähler potential as well as Euclidean D3-instanton superpotential. First, using the toric data for the aforementioned Swiss-Cheese Calabi-Yau and GLSM techniques, we obtain in the large volume limit, the geometric Kähler potential for the big (and small) divisor(s) in terms of derivatives of genus-two Siegel theta functions. Next, we show that as the mobile space-time filling D3-brane moves from a particular non-singular elliptic curve embedded in the Swiss-Cheese Calabi-Yau to another nonsingular elliptic curve, it is possible to obtain 10 12 GeV gravitino during the primordial inflationary era as well as, e.g., a T eV gravitino in the present era, within the same set up for the same volume of the Calabi-Yau stabilized at around 10 6 l (Σ B ) and extremizing the potential, we show that it is possible to obtain an O(1) g Y M from the wrapping of D7-branes on the big divisor due to competing contributions from the Wilson line moduli relative to the divisor volume modulus. To permit gaugino condensation, we take the rigid limit of the big divisor by considering zero sections of the normal bundle of the same -the same being justified by the extremization of the potential. For the purposes of calculation of the gaugino masses, matter moduli masses and soft supersymmetry breaking parameters, we restrict the mobile D3-brane to the big divisor -this has the additional advantage of nullification of the superpotential generated from gaugino condensation. With the inclusion of the matter moduli corresponding to the position moduli of the mobile D3-brane and the Wilson line moduli corresponding to the D7-branes, we obtain gaugino masses of the order of gravitino mass and the matter fields' masses to be enhanced relative to the gravitino mass. The anomaly-mediated gaugino masses are found to be suppressed relative to the gravity-mediated gaugino masses by the standard loop factor. New non-zero contributions to the µ-terms, though sub-dominant in the large volume limit, are obtained from section of the (small) divisor bundle encoding information about the ED3-instanton fluctuation determinant. filling D3-brane and the Wilson line moduli. There is a (near) universality in the masses,μ-parameters, Yukawa couplings and theμB-terms for the D3-brane position moduli -the Higgs doublet in our constr...

We present concrete embeddings of fibre inflation models in globally consistent type IIB Calabi-Yau orientifolds with closed string moduli stabilisation. After performing a systematic search through the existing list of toric Calabi-Yau manifolds, we find several examples that reproduce the minimal setup to embed fibre inflation models. This involves Calabi-Yau manifolds with h 1,1 = 3 which are K3 fibrations over a P 1 base with an additional shrinkable rigid divisor. We then provide different consistent choices of the underlying brane set-up which generate a non-perturbative superpotential suitable for moduli stabilisation and string loop corrections with the correct form to drive inflation. For each Calabi-Yau orientifold setting, we also compute the effect of higher derivative contributions and study their influence on the inflationary dynamics.

We argue that in type IIB LVS string models, after including the leading order moduli stabilisation effects, the moduli space for the remaining flat directions is compact due the Calabi-Yau Kähler cone conditions. In cosmological applications, this gives an inflaton field range which is bounded from above, in analogy with recent results from the weak gravity and swampland conjectures. We support our claim by explicitly showing that it holds for all LVS vacua with h 1,1 = 3 obtained from 4-dimensional reflexive polytopes. In particular, we first search for all Calabi-Yau threefolds from the Kreuzer-Skarke list with h 1,1 = 2, 3 and 4 which allow for LVS vacua, finding several new LVS geometries which were so far unknown. We then focus on the h 1,1 = 3 cases and show that the Kähler cones of all toric hypersurface threefolds force the effective 1-dimensional LVS moduli space to be compact. We find that the moduli space size can generically be trans-Planckian only for K3 fibred examples.

In order to support the odd moduli in models of (type IIB) string compactification, we classify the Calabi-Yau threefolds with h 1,1 ≤ 4 which exhibit pairs of identical divisors, with different line-bundle charges, mapping to each other under possible divisor exchange involutions. For this purpose, the divisors of interest are identified as completely rigid surface, Wilson surface, K3 surface and some other deformation surfaces. Subsequently, various possible exchange involutions are examined under the symmetry of Stanley-Reisner Ideal. In addition, we search for the Calabi-Yau theefolds which contain a divisor with several disjoint components. Under certain reflection involution, such spaces also have nontrivial odd components in (1,1)-cohomology class. String compactifications on such Calabi-Yau orientifolds with non-zero h 1,1 − (CY 3 /σ) could be promising for concrete model building in both particle physics and cosmology. In the spirit of using such Calabi-Yau orientifolds in the context of LARGE volume scenario, we also present some concrete examples of (strong/weak) swiss-cheese type volume form. 1