R-Matrix Formulation of KP Hierarchies and their Gauge Equivalence

The Adler-Kostant-Symes $R$-bracket scheme is applied to the algebra of pseudo-differential operators to relate the three integrable hierarchies: KP and its two modifications, known as nonstandard integrable models. All three hierarchies are shown to be equivalent and connection is established in the form of a symplectic gauge transformation. This construction results in a new representation of the W-infinity algebras in terms of 4 bosonic fields.Comment: 13 pages, Latex, CERN-TH.6627/9

Dynamically generated inflationary two-field potential via non-Riemannian volume forms

We consider a simple model of modified gravity interacting with a single scalar field $\varphi$ with weakly coupled exponential potential within the framework of non-Riemannian spacetime volume-form formalism. The specific form of the action is fixed by the requirement of invariance under global Weyl-scale symmetry. Upon passing to the physical Einstein frame we show how the non-Riemannian volume elements create a second canonical scalar field $u$ and dynamically generate a non-trivial two-scalar-field potential $U_{\rm eff}(u,\varphi)$ with two remarkable features: (i) it possesses a large flat region for large $u$ describing a slow-roll inflation; (ii) it has a stable low-lying minimum w.r.t. $(u,\varphi)$ representing the dark energy density in the "late universe". We study the corresponding two-field slow-roll inflation and show that the pertinent slow-roll inflationary curve $\varphi = \varphi(u)$ in the two-field space $(u,\varphi)$ has a very small curvature, i.e., $\varphi$ changes very little during the inflationary evolution of $u$ on the flat region of $U_{\rm eff}(u,\varphi)$. Explicit expressions are found for the slow-roll parameters which differ from those in the single-field inflationary counterpart. Numerical solutions for the scalar spectral index and the tensor-to-scalar ratio are derived agreeing with the observational data.Comment: 13 pages. 2 Fig. arXiv admin note: text overlap with arXiv:1906.06691 , v.2 14 pages, typos corrected, additional explanation

Weyl-Conformally-Invariant Lightlike p-Brane Theories: New Aspects in Black Hole Physics and Kaluza-Klein Dynamics

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In D=4 the WILL-membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on (``straddles'') the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps non-trivially around the compact (internal)dimensions and still describes massless mode dynamics in the non-compact (space-time) dimensions. Due to nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with non-trivial angular momentum, and with linear dependence between energy and angular momentum.Comment: 28 pages, published versio

Fully Explorable Horned Particles Hiding Charge

The charge-hiding effect by a horned particle, which was studied for the case where gravity/gauge-field system is self-consistently interacting with a charged lightlike brane (LLB) as a matter source, is now studied for the case of a time like brane. From the demand that no surfaces of infinite coordinate time redshift (horizons) appear in the problem we are lead now to a completly explorable horned particle space for traveller that goes through the horned particle (as was the case for the LLB) but now also in addition to this, the horned region is fully visible to a static external observer. This requires negative surface energy density for the shell sitting at the throat. We study a gauge field subsystem which is of a special non-linear form containing a square-root of the Maxwell term and which previously has been shown to produce a QCD-like confining gauge field dynamics in flat space-time. The condition of finite energy of the system or asymptotic flatness on one side of the horned particle implies that the charged object sitting at the throat expels all the flux it produces into the other side of the horned particle, which turns out to be of a "tube-like" nature. An outside observer in the asymptotically flat universe detects, therefore, apparently neutral object. The hiding of the electric flux behind the tube-like region of a horned particle is the only possible way that a truly charged particle can still be of finite energy, in a theory that in flat space describes confinement. This points to the physical relevance of such solutions, even though there is the need of negative energy density at the throat of the horned particle, which can be of quantum mechanical origin.Comment: The new version has been accepted for publication in Classical and Quantum Gravity. Title changed to "Fully Explorable Horned Particles Hiding Charge". Horned Particles terminology is used now instead of "wormholes" to dscribe the solutions here. arXiv admin note: text overlap with arXiv:1108.373