Euclidean-signature Supergravities, Dualities and Instantons

We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.Comment: Latex, 50 pages, typos corrected and references adde

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

Symmetries in M-theory: Monsters, Inc

We will review the algebras which have been conjectured as symmetries in M-theory. The Borcherds algebras, which are the most general Lie algebras under control, seem natural candidates.Comment: 6 pages, talk given by PHL at Cargese 200

Proactive monitoring system for investment projects: mathematical support

Using mathematical based evaluation systems will help ranking investment projects to select the best and most promising among the available. Based on the study, the author sees it best to apply mathematical models and concentrate on conceptual investment projects for reducing monitoring and evaluation costs, as well as initial development costs. Optimal ways to form expert groups for investment project proactive monitoring is offered in conclusio

Switchable lasing in coupled multimode microcavities

We propose the new concept of a switchable multimode microlaser. As a generic, realistic model of a multimode microresonator a system of two coupled defects in a two-dimensional photonic crystal is considered. We demonstrate theoretically that lasing of the cavity into one selected resonator mode can be caused by injecting an appropriate optical pulse at the onset of laser action (injection seeding). Temporal mode-to-mode switching by re-seeding the cavity after a short cool-down period is demonstrated by direct numerical solution. A qualitative analytical explanation of the mode switching in terms of the laser bistability is presented.Comment: Accepted for publication in Physical Review Letters. Published, somewhat shortened versio

On the sigma-model structure of type IIA supergravity action in doubled field approach

In this letter we describe how to string together the doubled field approach by Cremmer, Julia, Lu and Pope with Pasti-Sorokin-Tonin technique to construct the sigma-model-like action for type IIA supergravity. The relation of the results with that of obtained in the context of searching for Superstring/M-theory hidden symmetry group is discussed.Comment: 9 pp, LATEX; published in JETP Let

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

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

Black Holes on Cylinders

We take steps toward constructing explicit solutions that describe non-extremal charged dilatonic branes of string/M-theory with a transverse circle. Using a new coordinate system we find an ansatz for the solutions with only one unknown function. We show that this function is independent of the charge and our ansatz can therefore also be used to construct neutral black holes on cylinders and near-extremal charged dilatonic branes with a transverse circle. For sufficiently large mass $M > M_c$ these solutions have a horizon that connects across the cylinder but they are not translationally invariant along the circle direction. We argue that the neutral solution has larger entropy than the neutral black string for any given mass. This means that for $M > M_c$ the neutral black string can gain entropy by redistributing its mass to a solution that breaks translational invariance along the circle, despite the fact that it is classically stable. We furthermore explain how our construction can be used to study the thermodynamics of Little String Theory.Comment: latex, 68 pages, 4 figures. v2: Typos fixed, argument about \chi corrected in sec. 7.4, discussion of space of physical solutions corrected and clarified in sec. 9; v3: v=\pi clarified, typos fixed, figure 1 change