D-branes from Matrix Factorizations

B-type D-branes can be obtained from matrix factorizations of the Landau-Ginzburg superpotential. We here review this promising approach to learning about the spacetime superpotential of Calabi-Yau compactifications. We discuss the grading of the D-branes, and present applications in two examples: the two-dimensional torus, and the quintic.Comment: 10 pages. Talk given by J.W. at Strings '04, June 28-July 2, Pari

D-branes on the Quintic

We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed by Recknagel and Schomerus, to begin sketching a picture of D-branes in the stringy regime. We also make first steps towards computing superpotentials on the D-brane world-volumes.Comment: harvmac, 78 pp (v3: notes added and improved discussion of an example

Orientifolds of Gepner Models

We systematically construct and study Type II Orientifolds based on Gepner models which have N=1 supersymmetry in 3+1 dimensions. We classify the parity symmetries and construct the crosscap states. We write down the conditions that a configuration of rational branes must satisfy for consistency (tadpole cancellation and rank constraints) and spacetime supersymmetry. For certain cases, including Type IIB orientifolds of the quintic and a two parameter model, one can find all solutions in this class. Depending on the parity, the number of vacua can be large, of the order of 10^{10}-10^{13}. For other models, it is hard to find all solutions but special solutions can be found -- some of them are chiral. We also make comparison with the large volume regime and obtain a perfect match. Through this study, we find a number of new features of Type II orientifolds, including the structure of moduli space and the change in the type of O-planes under navigation through non-geometric phases.Comment: 142 page

Tree roots in a changing world

Globally, forests cover 4 billion hectares or 30% of the Earth's land surface, and 20%-40% of the forest biomass is made up of roots. Roots play a key role for trees: they take up water and nutrients from the soil, store carbon (C) compounds, and provide physical stabilization. Estimations from temperate forests of Central Europe reveal that C storage in trees accounts for about 110 t C ha−1, of which 26 t C ha−1 is in coarse roots and 1.2 t C ha−1 is in fine roots. Compared with soil C, which is about 65 t C ha−1 (without roots), the contribution of the root C to the total belowground C pool is about 42%. Flux of C into soils by plant litter (stemwood excluded) compared with the total soil C pool, however, is relatively small (4.4 t C ha−1 year−1) with the coarse and fine roots each contributing about 20%. Elevated CO2 concentrations and N depositions lead to increased plant biomass, including that of roots. Recent analysis in experiments with elevated CO2 concentrations have shown increases of the forest net primary productivity by about 23%, and, in the case of poplars, an increase of the standing root biomass by about 62%. The turnover of fine roots is also positively influenced by elevated CO2 concentrations and can be increased in poplars by 25%-45%. A recently established international platform for scientists working on woody root processes, COST action E38, allows the exchange of information, ideas, and personnel, and it has the aim to identify knowledge gaps and initiate future collaborations and research activitie

Matrix Factorizations, D-Branes and their Deformations

We review in elementary, non-technical terms the description of topological B-type of D-branes in terms of boundary Landau-Ginzburg theory, as well as some applications.Comment: 20p, 5 figs, Proceedings of Cargese school on string theory, 200

On D0-branes in Gepner models

We show why and when D0-branes at the Gepner point of Calabi-Yau manifolds given as Fermat hypersurfaces exist.Comment: 22 pages, substantial improvements in sections 2 and 3, references added, version to be publishe

Tachyon Condensation on the Elliptic Curve

We use the framework of matrix factorizations to study topological B-type D-branes on the cubic curve. Specifically, we elucidate how the brane RR charges are encoded in the matrix factors, by analyzing their structure in terms of sections of vector bundles in conjunction with equivariant R-symmetry. One particular advantage of matrix factorizations is that explicit moduli dependence is built in, thus giving us full control over the open-string moduli space. It allows one to study phenomena like discontinuous jumps of the cohomology over the moduli space, as well as formation of bound states at threshold. One interesting aspect is that certain gauge symmetries inherent to the matrix formulation lead to a non-trivial global structure of the moduli space. We also investigate topological tachyon condensation, which enables us to construct, in a systematic fashion, higher-dimensional matrix factorizations out of smaller ones; this amounts to obtaining branes with higher RR charges as composites of ones with minimal charges. As an application, we explicitly construct all rank-two matrix factorizations.Comment: 69p, 6 figs, harvmac; v2: minor change

On D-branes from Gauged Linear Sigma Models

We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear sigma model limit of the corresponding Calabi-Yau manifold, where we also find that we need to add a contact term on the boundary. These considerations enable to us to derive the boundary conditions in the full gauged linear sigma model, including the addition of the appropriate boundary contact terms, such that these boundary conditions have the correct non-linear sigma model limit. Most of the analysis is for the case of Calabi-Yau manifolds with one Kahler modulus (including those corresponding to hypersurfaces in weighted projective space), though we comment on possible generalizations.Comment: 31+1 pages; LaTex; (v2) Results now extended to include weighted projective spaces. Typos correcte

Chiral Supersymmetric Gepner Model Orientifolds

We explicitly construct A-type orientifolds of supersymmetric Gepner models. In order to reduce the tadpole cancellation conditions to a treatable number we explicitly work out the generic form of the one-loop Klein bottle, annulus and Moebius strip amplitudes for simple current extensions of Gepner models. Equipped with these formulas, we discuss two examples in detail to provide evidence that in this setting certain features of the MSSM like unitary gauge groups with large enough rank, chirality and family replication can be achieved.Comment: 37 pages, TeX (harvmac), minor changes, typos corrected, to appear in JHE