Duality Twists on a Group Manifold

We study duality-twisted dimensional reductions on a group manifold G, where the twist is in a group \tilde{G} and examine the conditions for consistency. We find that if the duality twist is introduced through a group element \tilde{g} in \tilde{G}, then the flat \tilde{G}-connection A =\tilde{g}^{-1} d\tilde{g} must have constant components M_n with respect to the basis 1-forms on G, so that the dependence on the internal coordinates cancels out in the lower dimensional theory. This condition can be satisfied if and only if M_n forms a representation of the Lie algebra of G, which then ensures that the lower dimensional gauge algebra closes. We find the form of this gauge algebra and compare it to that arising from flux compactifications on twisted tori. As an example of our construction, we find a new five dimensional gauged, massive supergravity theory by dimensionally reducing the eight dimensional Type II supergravity on a three dimensional unimodular, non-semi-simple, non-abelian group manifold with an SL(3,R) twist.Comment: 22 page

Quantum Mechanics of the Doubled Torus

We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce the number of degrees of freedom to the correct physical number. We consider this system from the point of view of constrained Hamiltonian dynamics. In this case the constraints are second class, and we can quantize on the constrained surface using Dirac brackets. We perform the quantization for a simple T-fold background and compare to results for the conventional non-doubled torus system. Finally, we formulate a consistent supersymmetric version of the doubled torus system, including supersymmetric constraints.Comment: 31 pages, 1 figure; v2: references added, minor corrections to final sectio

Canonical gravity in two time and two space dimensions

We describe a program for developing a canonical gravity in 2+2 dimensions (two time and two space dimensions). Our procedure is similar to the usual canonical gravity but with two times rather than just one time. Our work may be of particular interest as an alternative approach to loop quantum gravity in 2+2 dimensions.Comment: 13 pages, Latex, improved versio

The gauge algebra of double field theory and Courant brackets

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the doubled space and transform as vectors under T-duality. The gauge algebra defines a T-duality covariant bracket. For the case in which the parameters and fields are T-dual to ones that have momentum but no winding, we find the gauge transformations to all orders and show that the gauge algebra reduces to one obtained by Siegel. We show that the bracket for such restricted parameters is the Courant bracket. We explain how these algebras are realised as symmetries despite the failure of the Jacobi identity.Comment: 25 pages, LaTe

Environmental correlates of plant and invertebrate species richness in ponds

Ponds (lentic water bodies <2 ha) constitute a considerable biodiversity resource. Understanding the environmental factors that underlie this diversity is important in protecting and managing the habitat. We surveyed 425 ponds for biological and physical characteristics with 78 of those also surveyed for chemical characteristics. A total of 277 invertebrate species and 265 plant species were found. Species richness varied between 2 and 99 (mean 27.2 ± 0.6 SE) for invertebrates and 1 and 58 (mean 20.8 ± 0.4 SE) for plants. Generalised additive models were used to investigate variables that correlate with the species richness of plants and invertebrates, with additional models to investigate insect, Coleoptera, Odonata, Hemiptera, Trichoptera and Mollusca species richness. Models performed reasonably well for invertebrates in general (R 2 = 30.3%) but varied between lower-order invertebrate taxa (12.7–34.7%). Ponds with lower levels of shading and no history of drying contained higher numbers of species of plants and all invertebrate groups. Aquatic plant coverage positively correlated with species richness in all invertebrate groups apart from Trichoptera and the presence of fish was associated with high invertebrate species richness in all groups apart from Coleoptera. The addition of chemistry variables suggested non-linear relationships between oxygen demand and phosphate concentration and higher-order richness. We demonstrate that the composition of biological communities varies along with their species richness and that less diverse ponds are more variable compared to more diverse ponds. Variables positively correlated with richness of one taxon may be negatively correlated with that of another, making comprehensive management recommendations difficult. Promoting a high landscape-level pond biodiversity will involve the management of a high diversity of pond types within that landscape

Flux Compactifications of M-Theory on Twisted Tori

We find the bosonic sector of the gauged supergravities that are obtained from 11-dimensional supergravity by Scherk-Schwarz dimensional reduction with flux to any dimension D. We show that, if certain obstructions are absent, the Scherk-Schwarz ansatz for a finite set of D-dimensional fields can be extended to a full compactification of M-theory, including an infinite tower of Kaluza-Klein fields. The internal space is obtained from a group manifold (which may be non-compact) by a discrete identification. We discuss the symmetry algebra and the symmetry breaking patterns and illustrate these with particular examples. We discuss the action of U-duality on these theories in terms of symmetries of the D-dimensional supergravity, and argue that in general it will take geometric flux compactifications to M-theory on non-geometric backgrounds, such as U-folds with U-duality transition functions.Comment: Latex, 47 page

Generalised Geometry for M-Theory

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group $E_{d}$. This provides a framework for the discussion of M-theory solutions with flux. A different generalisation is to d-dimensional manifolds with a metric, 2-form gauge field and a set of p-forms for $p$ either odd or even on which there is a natural action of the group $E_{d+1}$. This is useful for type IIA or IIB string solutions with flux. Further generalisations give extended tangent bundles and extended spin bundles relevant for non-geometric backgrounds. Special structures that arise for supersymmetric backgrounds are discussed.Comment: 31 page

A Geometry for Non-Geometric String Backgrounds

A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirrors of flux compactifications, from reductions with duality twists and from asymmetric orbifolds. Strings in ` T-fold' backgrounds with a local $n$-torus fibration and T-duality transition functions in $O(n,n;\Z)$ are formulated in an enlarged space with a $T^{2n}$ fibration which is geometric, with spacetime emerging locally from a choice of a $T^n$ submanifold of each $T^{2n}$ fibre, so that it is a subspace or brane embedded in the enlarged space. T-duality acts by changing to a different $T^n$ subspace of $T^{2n}$. For a geometric background, the local choices of $T^n$ fit together to give a spacetime which is a $T^n$ bundle, while for non-geometric string backgrounds they do not fit together to form a manifold. In such cases spacetime geometry only makes sense locally, and the global structure involves the doubled geometry. For open strings, generalised D-branes wrap a $T^n$ subspace of each $T^{2n}$ fibre and the physical D-brane is the part of the part of the physical space lying in the generalised D-brane subspace.Comment: 28 Pages. Minor change

Space Shuttle: Static pressure distribution on Chrysler Corporation Space Division SERV booster configuration

A dual purpose test was conducted in the propulsion wind tunnel (PWT) to evaluate the performance of an aerospike engine, in the presence of a booster, and obtain forebody and base pressure distributions on the booster in which it is installed. The test item was a 2.5 percent scaled replica of the SERV booster employing a 5 percent spike length aerospike engine installed in the base region of the model. Cold flow air was used to simulate engine jet operation. Two booster configurations were investigated, one on which reentry aerospike engine thermal protection doors were installed, and another where the doors were removed. The data presented are representative of the latter configuration for a Mach number range of 0 to 1.25 at angles of attack of 0 and 8 degrees and 0 degrees angle of sideslip

Macroscopic Phase Coherence of Defective Vortex Lattices in Two Dimensions

The superfluid density is calculated theoretically for incompressible vortex lattices in two dimensions that have isolated dislocations quenched in by a random arrangement of pinned vortices. The latter are assumed to be sparse and to be fixed to material defects. It is shown that the pinned vortices act to confine a single dislocation of the vortex lattice along its glide plane. Plastic creep of the two-dimensional vortex lattice is thereby impeded, and macroscopic phase coherence results at low temperature in the limit of a dilute concentration of quenched-in dislocations.Comment: 18 pages, 1 figure, 1 table, new title, submitted to Physical Review