67 research outputs found
General solutions of the Monge-Amp\`{e}re equation in -dimensional space
It is shown that the general solution of a homogeneous Monge-Amp\`{e}re
equation in -dimensional space is closely connected with the exactly (but
only implicitly) integrable system
\frac {\partial \xi_{j}}{\partial x_0}+\sum_{k=1}^{n-1} \xi_{k} \frac
{\partial \xi_{j}}{\partial x_{k}}=0 \label{1}
Using the explicit form of solution of this system it is possible to
construct the general solution of the Monge-Amp\`{e}re equation.Comment: 8 page
Dirac-Born -Infeld Equations
Properties of the Dirac-Born-Infeld Lagrangian analogous to those of the
Nambu-Goto String are analysed. In particular the Lagrangian is shown to be
constant or zero on the space of solutions of the equations of motion if the
Lagrangian is taken to any power other than 1/2.Comment: 9 pages, LaTe
Universal Field Equations with Reparametrisation Invariance
New reparametrisation invariant field equations are constructed which
describe -brane models in a space of dimensions. These equations, like
the recently discovered scalar field equations in dimensions, are
universal, in the sense that they can be derived from an infinity of
inequivalent Lagrangians, but are nonetheless Lorentz (Euclidean) invariant.
Moreover, they admit a hierarchical structure, in which they can be derived by
a sequence of iterations from an arbitrary reparametrisation covariant
Lagrangian, homogeneous of weight one. None of the equations of motion which
appear in the hierarchy of iterations have derivatives of the fields higher
than the second. The new sequence of Universal equations is related to the
previous one by an inverse function transformation. The particular case of
, giving a new reparametrisation invariant string equation in 3 dimensions
is solved.Comment: 9page
Infinite series solutions of the symmetry equation for the dimensional continuous Toda chain
A sequence of solutions to the equation of symmetry for the continuous Toda
chain in dimensions is represented in explicit form. This fact leads to
the supposition that this equation is completely integrable.Comment: 9 pages, latex, no figure
Hamilton-Jacobi equations and Brane associated Lagrangians
This article seeks to relate a recent proposal for the association of a
covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi
formalism for strings and branes. It turns out that since in this special case,
the Hamiltonian depends only upon the momenta of the Jacobi fields and not the
fields themselves, it is the same as a Lagrangian, subject to a constancy
constraint. We find that the associated Lagrangians for strings or branes have
a covariant description in terms of the square root of the same Lagrangian. If
the Hamilton-Jacobi function is zero, rather than a constant, then it is in in
one dimension lower, reminiscent of the `holographic' idea. In the second part
of the paper, we discuss properties of these Lagrangians, which lead to what we
have called `Universal Field Equations', characteristic of covariant equations
of motion.Comment: 23 pages,LaTeX2e, clarified text, generalised proof in appendi
Effective theoretical approach of Gauge-Higgs unification model and its phenomenological applications
We derive the low energy effective theory of Gauge-Higgs unification (GHU)
models in the usual four dimensional framework. We find that the theories are
described by only the zero-modes with a particular renormalization condition in
which essential informations about GHU models are included. We call this
condition ``Gauge-Higgs condition'' in this letter. In other wards, we can
describe the low energy theory as the SM with this condition if GHU is a model
as the UV completion of the Standard Model. This approach will be a powerful
tool to construct realistic models for GHU and to investigate their low energy
phenomena.Comment: 18 pages, 2 figures; Two paragraphs discussing the applicable scope
of this approach are adde
Auxiliary Fields for Super Yang-Mills from Division Algebras
Division algebras are used to explain the existence and symmetries of various
sets of auxiliary fields for super Yang-Mills in dimensions .
(Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)Comment: 7 pages, plain TeX, CERN-TH.7470/9
Symmetry breaking from Scherk-Schwarz compactification
We analyze the classical stable configurations of an extra-dimensional gauge
theory, in which the extra dimensions are compactified on a torus. Depending on
the particular choice of gauge group and the number of extra dimensions, the
classical vacua compatible with four-dimensional Poincar\'e invariance and zero
instanton number may have zero energy. For SU(N) on a two-dimensional torus, we
find and catalogue all possible degenerate zero-energy stable configurations in
terms of continuous or discrete parameters, for the case of trivial or
non-trivial 't Hooft non-abelian flux, respectively. We then describe the
residual symmetries of each vacua.Comment: 24 pages, 1 figure, Section 4 modifie
Extension of geodesic algebras to continuous genus
Using the Penner--Fock parameterization for Teichmuller spaces of Riemann
surfaces with holes, we construct the string-like free-field representation of
the Poisson and quantum algebras of geodesic functions in the continuous-genus
limit. The mapping class group acts naturally in the obtained representation.Comment: 16 pages, submitted to Lett.Math.Phy
Dynamical symmetry breaking in Gauge-Higgs unification of 5D SUSY theory
We study the dynamical symmetry breaking in the gauge-Higgs unification of
the 5D SUSY theory, compactified on an orbifold, .
This theory identifies Wilson line degrees of freedoms as ``Higgs doublets''.
We consider and SU(6) models, in which the gauge
symmetries are reduced to and , respectively, through the
orbifolding boundary conditions. Quarks and leptons are bulk fields, so that
Yukawa interactions can be derived from the 5D gauge interactions. We estimate
the one loop effective potential of ``Higgs doublets'', and analyze the vacuum
structures in these two models. We find that the effects of bulk quarks and
leptons destabilize the suitable electro-weak vacuum. We show that the
introduction of suitable numbers of extra bulk fields possessing the suitable
representations can realize the appropriate electro-weak symmetry breaking.Comment: 15 pages, 4 figures;disscutions on Higgs quartic couplings adde
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