From Topology to Generalised Dimensional Reduction

In the usual procedure for toroidal Kaluza-Klein reduction, all the higher-dimensional fields are taken to be independent of the coordinates on the internal space. It has recently been observed that a generalisation of this procedure is possible, which gives rise to lower-dimensional ``massive'' supergravities. The generalised reduction involves allowing gauge potentials in the higher dimension to have an additional linear dependence on the toroidal coordinates. In this paper, we show that a much wider class of generalised reductions is possible, in which higher-dimensional potentials have additional terms involving differential forms on the internal manifold whose exterior derivatives yield representatives of certain of its cohomology classes. We consider various examples, including the generalised reduction of M-theory and type II strings on K3, Calabi-Yau and 7-dimensional Joyce manifolds. The resulting massive supergravities support domain-wall solutions that arise by the vertical dimensional reduction of higher-dimensional solitonic p-branes and intersecting p-branes.Comment: Latex, 24 pages, no figures, typo corrected, reference added and discussion of duality extende

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

English Slogans on Clothing: Linguistic Distinctiveness and Pragmatic Functions

A semantic analysis of inscriptions on T-shirts (slogans) as elements of everyday discourse is provided in the article. Attention is paid to slogans that convey meanings significant in youth communication. The scientific novelty of the presented work lies in the fact that for the first time the features of slogans placed on clothes are revealed, their content, pragmatic functions and lexical-semantic features, as well as the correlation of slogans with the linguistic personality of the owner of a T-shirt with an inscription are considered. The author revealed that the basic pragmatic functions of slogans are self-presentation, appeal and shocking. Each of these functions has a number of sub-functions. Self-presentation is the leading pragmatic function. It has been proved that slogans are important components of the modern socio-cultural environment, integral elements of the communication process, verbal markers of the peculiarities of a linguistic personality. The key features of the linguistic personality of a young man who implements communication through a slogan on clothes are openness to social contacts, demonstration of personal qualities, attitude towards others and towards society as a whole, social activity, dedication, unconventional worldview, innovative thinking

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

Structural Features of Metaphors in English Aphorisms within Philosophical Discourse

Structural analysis of aphorisms in philosophical discourse is conducted using a semantic-cognitive approach. The study focuses on aphorisms from Francis Bacon’s treatise “Novum Organum”. The objects, purposes, and bases of metaphorization are identified and classified, revealing phenomena that are objectified through metaphors and denote key areas of conceptualization in Bacon’s linguistic worldview. It is determined that the objects, sources, and bases of metaphorization are highly differentiated, highlighting personifications of the human image in Bacon’s linguistic worldview: the thinking, spiritual, social, and emotional aspects of humans. The majority of objects are anthropomorphic phenomena, including categories of moral order, age characteristics, intellectual abilities, and attributes of social interaction. The sources of metaphors touch upon the social role of humans, their physio-logical sensations from interacting with the environment, and demonstrate the empirical nature of the author’s linguistic personality. Among the sources of metaphors, the most representative group consists of naturalistic images. Francis Bacon refers to natural phenomena and objects as tools for creating complex philosophical concepts

Harmonic superpositions of non-extremal p-branes

The plot of allowed p and D values for p-brane solitons in D-dimensional supergravity is the same whether the solitons are extremal or non-extremal. One of the useful tools for relating different points on the plot is vertical dimensional reduction, which is possible if periodic arrays of p-brane solitons can be constructed. This is straightforward for extremal p-branes, since the no-force condition allows arbitrary multi-centre solutions to be constructed in terms of a general harmonic function on the transverse space. This has also been shown to be possible in the special case of non-extremal black holes in D=4 arrayed along an axis. In this paper, we extend previous results to include multi-scalar black holes, and dyonic black holes. We also consider their oxidation to higher dimensions, and we discuss general procedures for constructing the solutions, and studying their symmetries.Comment: Latex, 23 page

Direct amplitude-phase near-field observation of higher-order anapole states

Anapole states associated with the resonant suppression of electric-dipole scattering exhibit minimized extinction and maximized storage of electromagnetic energy inside a particle. Using numerical simulations, optical extinction spectroscopy and amplitude-phase near-field mapping of silicon dielectric disks, we demonstrate high-order anapole states in the near-infrared wavelength range (900-1700 nm). We develop the procedure for unambiguously identifying anapole states by monitoring the normal component of the electric near-field and experimentally detect the first two anapole states as verified by far-field extinction spectroscopy and confirmed with the numerical simulations. We demonstrate that higher order anapole states possess stronger energy concentration and narrower resonances, a remarkable feature that is advantageous for their applications in metasurfaces and nanophotonics components, such as non-linear higher-harmonic generators and nanoscale lasers