From p-branes to Cosmology

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M-theory. We discuss two different ways in which extremal p-branes can be generalised to non-extremal ones, and show how wide classes of recently discussed cosmological models can be mapped into non-extremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalised dimensional reduction of string theory or M-theory.Comment: Latex, 24 pages, no figur

U-duality as General Coordinate Transformations, and Spacetime Geometry

We show that the full global symmetry groups of all the D-dimensional maximal supergravities can be described in terms of the closure of the internal general coordinate transformations of the toroidal compactifications of D=11 supergravity and of type IIB supergravity, with type IIA/IIB T-duality providing an intertwining between the two pictures. At the quantum level, the part of the U-duality group that corresponds to the surviving discretised internal general coordinate transformations in a given picture leaves the internal torus invariant, while the part that is not described by internal general coordinate transformations can have the effect of altering the size or shape of the internal torus. For example, M-theory compactified on a large torus T^n can be related by duality to a compactification on a small torus, if and only if n\ge 3. We also discuss related issues in the toroidal compactification of the self-dual string to D=4. An appendix includes the complete results for the toroidal reduction of the bosonic sector of type IIB supergravity to arbitrary dimensions D\ge3.Comment: Latex, 28 page

Compactifications with S-Duality Twists

We consider generalised Scherk Schwarz reductions of supergravity and superstring theories with twists by electromagnetic dualities that are symmetries of the equations of motion but not of the action, such as the S-duality of D=4, N=4 super-Yang-Mills coupled to supergravity. The reduction cannot be done on the action itself, but must be done either on the field equations or on a duality invariant form of the action, such as one in the doubled formalism in which potentials are introduced for both electric and magnetic fields. The resulting theory in odd-dimensions has massive form fields satisfying a self-duality condition $dA \sim m*A$. We construct such theories in D=3,5,7.Comment: Latex, 26 pages. References adde

Multiplet Structures of BPS Solitons

There exist simple single-charge and multi-charge BPS p-brane solutions in the D-dimensional maximal supergravities. From these, one can fill out orbits in the charge vector space by acting with the global symmetry groups. We give a classification of these orbits, and the associated cosets that parameterise them.Comment: Latex, 34 pages, comments and reference adde

Timelike Hopf Duality and Type IIA^* String Solutions

The usual T-duality that relates the type IIA and IIB theories compactified on circles of inversely-related radii does not operate if the dimensional reduction is performed on the time direction rather than a spatial one. This observation led to the recent proposal that there might exist two further ten-dimensional theories, namely type IIA^* and type IIB^*, related to type IIB and type IIA respectively by a timelike dimensional reduction. In this paper we explore such dimensional reductions in cases where time is the coordinate of a non-trivial U(1) fibre bundle. We focus in particular on situations where there is an odd-dimensional anti-de Sitter spacetime AdS_{2n+1}, which can be described as a U(1) bundle over \widetilde{CP}^n, a non-compact version of CP^n corresponding to the coset manifold SU(n,1)/U(n). In particular, we study the AdS_5\times S^5 and AdS_7\times S^4 solutions of type IIB supergravity and eleven-dimensional supergravity. Applying a timelike Hopf T-duality transformation to the former provides a new solution of the type IIA^* theory, of the form \widetilde{CP}^2\times S^1\times S^5. We show how the Hopf-reduced solutions provide further examples of ``supersymmetry without supersymmetry.'' We also present a detailed discussion of the geometrical structure of the Hopf-fibred metric on AdS_{2n+1}, and its relation to the horospherical metric that arises in the AdS/CFT correspondence.Comment: Latex, 26 page

The many faces of OSp(1|32)

We show that the complete superalgebra of symmetries, including central charges, that underlies F-theories, M-theories and type II string theories in dimensions 12, 11 and 10 of various signatures correspond to rewriting of the same OSp(1|32) algebra in different covariant ways. One only has to distinguish the complex and the unique real algebra. We develop a common framework to discuss all signatures theories by starting from the complex form of OSp(1|32). Theories are distinguished by the choice of basis for this algebra. We formulate dimensional reductions and dualities as changes of basis of the algebra. A second ingredient is the choice of a real form corresponding to a specific signature. The existence of the real form of the algebra selects preferred spacetime signatures. In particular, we show how the real d=10 IIA and IIB superalgebras for various signatures are related by generalized T-duality transformations that not only involve spacelike but also timelike directions. A third essential ingredient is that the translation generator in one theory plays the role of a central charge operator in the other theory. The identification of the translation generator in these algebras leads to the star algebras of Hull, which are characterized by the fact that the positive definite energy operator is not part of the translation generators. We apply our results to discuss different T-dual pictures of the D-instanton solution of Euclidean IIB supergravity.Comment: 30 pages, Latex, using lscape.st

Duality symmetric massive type II theories in D=8 and D=6

We study $T^2$ compactification of massive type IIA supergravity in presence of possible Ramond-Ramond (RR) background fluxes. The resulting theory in D=8 is shown to possess full $SL(2,R)\times SL(2,R)$ T-duality symmetry similar to the massless case. It is shown that elements of duality symmetry interpolate between massive type IIA compactified on $T^2$ and ordinary type IIA compactified on $T^2$ with RR 2-form flux. We also discuss relationship between M-theory vacua and massive type IIA vacua. The D8-brane is found to correspond to M-theory `pure gravity' solution which is a direct product of 7-dimensional Minkowski space and a 4-dimensional instanton. We also construct D6-D8 bound state which preserves 1/2 supersymmetries. We then discuss massive IIA compactification on $T^4$ and point out that when all possible RR fluxes on $T^4$ are turned on the six-dimensional theory appears to assume a nice SO(4,4) invariant form.Comment: 19 pages, JHEP3, typos fixed, references added; v2: small correction in eq.(5.3), published in JHE

Monotonic properties of the shift and penetration factors

We study derivatives of the shift and penetration factors of collision theory with respect to energy, angular momentum, and charge. Definitive results for the signs of these derivatives are found for the repulsive Coulomb case. In particular, we find that the derivative of the shift factor with respect to energy is positive for the repulsive Coulomb case, a long anticipated but heretofore unproven result. These results are closely connected to the properties of the sum of squares of the regular and irregular Coulomb functions; we also present investigations of this quantity.Comment: 13 pages, 1 figur

Untangling the Conceptual Isssues Raised in Reydon and Scholz’s Critique of Organizational Ecology and Darwinian Populations

Reydon and Scholz raise doubts about the Darwinian status of organizational ecology by arguing that Darwinian principles are not applicable to organizational populations. Although their critique of organizational ecology’s typological essentialism is correct, they go on to reject the Darwinian status of organizational populations. This paper claims that the distinction between replicators and interactors, raised in modern philosophy of biology but not discussed by Reydon and Scholz, points the way forward for organizational ecologists. It is possible to conceptualise evolving Darwinian populations providing the inheritance mechanism is appropriately specified. By this approach, adaptation and selection are no longer dichotomised, and the evolutionary significance of knowledge transmission is highlightedPeer reviewe