Heterotic Flux Attractors

We find attractor equations describing moduli stabilization for heterotic compactifications with generic SU(3)-structure. Complex structure and K\"ahler moduli are treated on equal footing by using SU(3)xSU(3)-structure at intermediate steps. All independent vacuum data, including VEVs of the stabilized moduli, is encoded in a pair of generating functions that depend on fluxes alone. We work out an explicit example that illustrates our methods.Comment: 37 pages, references and clarifications adde

Smeared versus localised sources in flux compactifications

We investigate whether vacuum solutions in flux compactifications that are obtained with smeared sources (orientifolds or D-branes) still survive when the sources are localised. This seems to rely on whether the solutions are BPS or not. First we consider two sets of BPS solutions that both relate to the GKP solution through T-dualities: (p+1)-dimensional solutions from spacetime-filling Op-planes with a conformally Ricci-flat internal space, and p-dimensional solutions with Op-planes that wrap a 1-cycle inside an everywhere negatively curved twisted torus. The relation between the solution with smeared orientifolds and the localised version is worked out in detail. We then demonstrate that a class of non-BPS AdS_4 solutions that exist for IASD fluxes and with smeared D3-branes (or analogously for ISD fluxes with anti-D3-branes) does not survive the localisation of the (anti) D3-branes. This casts doubts on the stringy consistency of non-BPS solutions that are obtained in the limit of smeared sources.Comment: 23 pages; v2: minor corrections, added references, version published in JHE

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Microalgae production in fresh market wastewater and its utilization as a protein substitute in formulated fish feed for oreochromis spp.

Rapid growing of human population has led to increasing demand of aquaculture production. Oreochromis niloticus or known as tilapia is one of the most globally cultured freshwater fish due to its great adaptation towards extreme environment. Besides, farming of tilapia not only involves small scales farming for local consumption but also larger scales for international market which contributes to a foreign currency earning. Extensive use of fishmeal as feed for fish and for other animals indirectly caused an increasing depletion of the natural resource and may consequently cause economic and environmental unstable. Microalgae biomass seems to be a promising feedstock in aquaculture industry. It can be used for many purposes such as live food for fish larvae and dried microalgae to substitute protein material in fish feed. The microalgae replacement in fish feed formulation as protein alternative seem potentially beneficial for long term aqua-business sustainability. The present chapter discussed the potential of microalgae as an alternative nutrition in fish feed formulations, specifically Tilapia

Hypermoduli Stabilization, Flux Attractors, and Generating Functions

We study stabilization of hypermoduli with emphasis on the effects of generalized fluxes. We find a class of no-scale vacua described by ISD conditions even in the presence of geometric flux. The associated flux attractor equations can be integrated by a generating function with the property that the hypermoduli are determined by a simple extremization principle. We work out several orbifold examples where all vector moduli and many hypermoduli are stabilized, with VEVs given explicitly in terms of fluxes.Comment: 45 pages, no figures; Version submitted to JHE

Charting the landscape of N=4 flux compactifications

We analyse the vacuum structure of isotropic Z_2 x Z_2 flux compactifications, allowing for a single set of sources. Combining algebraic geometry with supergravity techniques, we are able to classify all vacua for both type IIA and IIB backgrounds with arbitrary gauge and geometric fluxes. Surprisingly, geometric IIA compactifications lead to a unique theory with four different vacua. In this case we also perform the general analysis allowing for sources compatible with minimal supersymmetry. Moreover, some relevant examples of type IIB non-geometric compactifications are studied. The computation of the full N=4 mass spectrum reveals the presence of a number of non-supersymmetric and nevertheless stable AdS_4 vacua. In addition we find a novel dS_4 solution based on a non-semisimple gauging.Comment: Minor corrections and references added. Version published in JHE

Exceptional Flux Compactifications

We consider type II (non-)geometric flux backgrounds in the absence of brane sources, and construct their explicit embedding into maximal gauged D=4 supergravity. This enables one to investigate the critical points, mass spectra and gauge groups of such backgrounds. We focus on a class of type IIA geometric vacua and find a novel, non-supersymmetric and stable AdS vacuum in maximal supergravity with a non-semisimple gauge group. Our construction relies on a non-trivial mapping between SL(2) x SO(6,6) fluxes, SU(8) mass spectra and gaugings of E7(7) subgroups.Comment: 51 pages, 2 figures and 4 tables. v3: change of SO(6,6) spinorial conventions, published versio

Electroweak Baryogenesis and Dark Matter with an approximate R-symmetry

It is well known that R-symmetric models dramatically alleviate the SUSY flavor and CP problems. We study particular modifications of existing R-symmetric models which share the solution to the above problems, and have interesting consequences for electroweak baryogenesis and the Dark Matter (DM) content of the universe. In particular, we find that it is naturally possible to have a strongly first-order electroweak phase transition while simultaneously relaxing the tension with EDM experiments. The R-symmetry (and its small breaking) implies that the gauginos (and the neutralino LSP) are pseudo-Dirac fermions, which is relevant for both baryogenesis and DM. The singlet superpartner of the U(1)_Y pseudo-Dirac gaugino plays a prominent role in making the electroweak phase transition strongly first-order. The pseudo-Dirac nature of the LSP allows it to behave similarly to a Dirac particle during freeze-out, but like a Majorana particle for annihilation today and in scattering against nuclei, thus being consistent with current constraints. Assuming a standard cosmology, it is possible to simultaneously have a strongly first-order phase transition conducive to baryogenesis and have the LSP provide the full DM relic abundance, in part of the allowed parameter space. However, other possibilities for DM also exist, which are discussed. It is expected that upcoming direct DM searches as well as neutrino signals from DM annihilation in the Sun will be sensitive to this class of models. Interesting collider and Gravity-wave signals are also briefly discussed.Comment: 50 pages, 10 figure

Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds

We consider type IIB flux compactifications on six-dimensional SU(2)-structure manifolds with O5- and O7-planes. These six-dimensional spaces allow not only for F_3 and H_3 fluxes but also for F_1 and F_5 fluxes. We derive the four-dimensional N=1 scalar potential for such compactifications and present one explicit example of a fully stabilized AdS vacuum with large volume and small string coupling. We then discuss cosmological aspects of these compactifications and derive several no-go theorems that forbid dS vacua and slow-roll inflation under certain conditions. We also study concrete examples of cosets and twisted tori and find that our no-go theorems forbid dS vacua and slow-roll inflation in all but one of them. For the latter we find a dS critical point with \epsilon numerically zero. However, the point has two tachyons and eta-parameter \eta \approx -3.1.Comment: 35 pages + appendices, LaTeX2e; v2: numerical dS extremum added, typos corrected, references adde