25,254 research outputs found
One-dimensional topologically nontrivial solutions in the Skyrme model
We consider the Skyrme model using the explicit parameterization of the
rotation group SO(3) through elements of its algebra. Topologically nontrivial
solutions already arise even in the one-dimensional case because the
fundamental group of SO(3) is Z_2. We explicitly find and analyze
one-dimensional static solutions. Among them, there are topologically
nontrivial solutions with finite energy among them. We propose a new class of
projective models whose target spaces are arbitrary real projective spaces
RP^d.Comment: 15 pages, 1 ps figure, added reference
Minimal Supergravity and the supersymmetry of Arnold-Beltrami Flux branes
In this paper we study some properties of the newly found Arnold-Beltrami
flux-brane solutions to the minimal supergravity. To this end we first
single out the appropriate Free Differential Algebra containing both a gauge
-form and a gauge -form : then we
present the complete rheonomic parametrization of all the generalized
curvatures. This allows us to identify two-brane configurations with
Arnold-Beltrami fluxes in the transverse space with exact solutions of
supergravity and to analyze the Killing spinor equation in their background. We
find that there is no preserved supersymmetry if there are no additional
translational Killing vectors. Guided by this principle we explicitly construct
Arnold-Beltrami flux two-branes that preserve , and of the
original supersymmetry. Two-branes without fluxes are instead BPS states and
preserve supersymmetry. For each two-brane solution we carefully study
its discrete symmetry that is always given by some appropriate crystallographic
group . Such symmetry groups are transmitted to the
gauge theories on the brane world--volume that occur in the gauge/gravity
correspondence. Furthermore we illustrate the intriguing relation between gauge
fluxes in two-brane solutions and hyperinstantons in topological
sigma-models.Comment: 56 pages, LaTeX source, 8 jpg figures, typos correcte
The Yang-Baxter equation for PT invariant nineteen vertex models
We study the solutions of the Yang-Baxter equation associated to nineteen
vertex models invariant by the parity-time symmetry from the perspective of
algebraic geometry. We determine the form of the algebraic curves constraining
the respective Boltzmann weights and found that they possess a universal
structure. This allows us to classify the integrable manifolds in four
different families reproducing three known models besides uncovering a novel
nineteen vertex model in a unified way. The introduction of the spectral
parameter on the weights is made via the parameterization of the fundamental
algebraic curve which is a conic. The diagonalization of the transfer matrix of
the new vertex model and its thermodynamic limit properties are discussed. We
point out a connection between the form of the main curve and the nature of the
excitations of the corresponding spin-1 chains.Comment: 43 pages, 6 figures and 5 table
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