Generalised G2G_2-structures and type IIB superstrings

The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group $SO(d,d)$ of the vector bundle $T^d\oplus T^{d*}$ to a special subgroup. In this article we show that compactification of IIB superstring vacua on 7-manifolds with two covariantly constant spinors leads to a generalised $G_2$-structure associated with a reduction from SO(7,7) to $G_2\times G_2$. We also consider compactifications on 6-manifolds where analogously we obtain a generalised SU(3)-structure associated with $SU(3)\times SU(3)$, and show how these relate to generalised $G_2$-structures.Comment: 14 pages, v2: Section 4 rewritten and references added, final version of the paper to appear in JHE

Fluxes in M-theory on 7-manifolds: G_2-, SU(3)- and SU(2)-structures

We consider compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes, which leave at least four supercharges unbroken. Supersymmetric vacua admit G-structures and we discuss the cases of G_2-, SU(3)- as well as SU(2)-structures. We derive the constraints on the fluxes imposed by supersymmetry and determine the flux components that fix the resulting 4-dimensional cosmological constant (i.e. superpotential).Comment: 17 pages, contribution for the proceedings of: BW2003 Workshop, 29 Aug. - 02 Sept., 2003 Vrnjacka Banja, Serbi

N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_{\omega} X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.Comment: 24 pages; v2: reference adde

Superpotentials from flux compactifications of M-theory

In flux compactifications of M-theory a superpotential is generated whose explicit form depends on the structure group of the 7-dimensional internal manifold. In this note, we discuss superpotentials for the structure groups: G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For SU(3) structures, the non-zero flux components entering the superpotential describe an effective 1-dimensional model and a Chern-Simons model if there are SU(2) structures.Comment: 10 page

Background geometries in string and M-theory

In this thesis we consider background geometries resulting from string theory compactifications. In particular, we investigate supersymmetric vacuum spaces of supergravity theories and topological twisted sigma models by means of classical and generalised G-structures. In the first part we compactify 11d supergravity on seven-dimensional manifolds due to phenomenological reasons. A certain amount of supersymmetry forces the internal background to admit a classical SU(3)- or G2-structure. Especially, in the case that the four-dimensional space is maximally symmetric and four form fluxes are present we calculate the relation to the intrinsic torsion. The second and main part is two-fold. Firstly, we realise that generalised geometries on six-dimensional manifolds are a natural framework to study T-duality and mirror symmetry, in particular if the B-field is non-vanishing. An explicit mirror map is given and we apply this idea to the generalised formulation of a topological twisted sigma model. Implications of mirror symmetry are studied, e.g. observables and topological A- and B-branes. Secondly, we show that seven-dimensional NS-NS backgrounds in type II supergravity theories can be described by generalised G2-geometries. A compactification on six manifolds leads to a new structure. We call this geometry a generalised SU(3)-structure. We study the relation between generalised SU(3)- and G2-structures on six- and seven-manifolds and generalise the Hitchin-flow equations. Finally, we further develop the generalised SU(3)- and G2-structures via a constrained variational principle to incorporate also the remaining physical R-R fields

N=1 domain wall solutions of massive type II supergravity and the issue of mirror symmetry

We report on Domain Wall solution of Calabi-Yau compactifications with general fluxes and their application to the study of mirror symmetry in generalized backgrounds. We address, in particular, to the issue of magnetic NSNS fluxes. We show that the Domain Wall gradient flow equations can be interpreted as a set of generalized Hitchin's flow equations of a manifold with SU(3)x SU(3) structure fibered along the direction transverse to the Domain wall.Comment: To appear in the proceedings of 2nd RTN Network Workshop and Midterm Meeting: Constituents, Fundamental Forces and Symmetries of the Universe, Naples, Italy, 9-13 Oct 200

Ultradeep characterisation of translational sequence determinants refutes rare-codon hypothesis and unveils quadruplet base pairing of initiator tRNA and transcript

Translation is a key determinant of gene expression and an important biotechnological engineering target. In bacteria, 5′-untranslated region (5′-UTR) and coding sequence (CDS) are well-known mRNA parts controlling translation and thus cellular protein levels. However, the complex interaction of 5′-UTR and CDS has so far only been studied for few sequences leading to non-generalisable and partly contradictory conclusions. Herein, we systematically assess the dynamic translation from over 1.2 million 5′-UTR-CDS pairs in Escherichia coli to investigate their collective effect using a new method for ultradeep sequence-function mapping. This allows us to disentangle and precisely quantify effects of various sequence determinants of translation. We find that 5′-UTR and CDS individually account for 53% and 20% of variance in translation, respectively, and show conclusively that, contrary to a common hypothesis, tRNA abundance does not explain expression changes between CDSs with different synonymous codons. Moreover, the obtained large-scale data provide clear experimental evidence for a base-pairing interaction between initiator tRNA and mRNA beyond the anticodon-codon interaction, an effect that is often masked for individual sequences and therefore inaccessible to low-throughput approaches. Our study highlights the indispensability of ultradeep sequence-function mapping to accurately determine the contribution of parts and phenomena involved in gene regulation

Chemo-enzymatic cascades to produce cycloalkenes from bio-based resources

Engineered enzyme cascades offer powerful tools to convert renewable resources into value-added products. Man-made catalysts give access to new-to-nature reactivities that may complement the enzyme's repertoire. Their mutual incompatibility, however, challenges their integration into concurrent chemo-enzymatic cascades. Herein we show that compartmentalization of complex enzyme cascades within E. coli whole cells enables the simultaneous use of a metathesis catalyst, thus allowing the sustainable one-pot production of cycloalkenes from oleic acid. Cycloheptene is produced from oleic acid via a concurrent enzymatic oxidative decarboxylation and ring-closing metathesis. Cyclohexene and cyclopentene are produced from oleic acid via either a six- or eight-step enzyme cascade involving hydration, oxidation, hydrolysis and decarboxylation, followed by ring-closing metathesis. Integration of an upstream hydrolase enables the usage of olive oil as the substrate for the production of cycloalkenes. This work highlights the potential of integrating organometallic catalysis with whole-cell enzyme cascades of high complexity to enable sustainable chemistry

Supersymmetric D-branes and calibrations on general N=1 backgrounds

We study the conditions to have supersymmetric D-branes on general {\cal N}=1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3)\times SU(3) structure on T_M\oplus T^\star_M, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.Comment: 23 pages. Some improvements and clarifications, typos corrected and references added. v3: Version published in JHE