22,473 research outputs found
Topological defects in 1D elastic waves
It has been recently shown theoretically that a topological defect in a 1D
periodic potential may give rise to two localized states within the energy
gaps. In this work we present an experimental realization of this effect for
the case of torsional waves in elastic rods. We also show numerically that
three, or even more, localized states can be present if the parameters
characterizing the topological defect are suitably varied.Comment: 3 pages, 4 figures, accepted in Physica
Analytic Non-integrability in String Theory
Using analytic techniques developed for Hamiltonian dynamical systems we show
that a certain classical string configurations in AdS_5 x X_5 with X_5 in a
large class of Einstein spaces, is non-integrable. This answers the question of
integrability of string on such backgrounds in the negative. We consider a
string localized in the center of AdS_5 that winds around two circles in the
manifold X_5.Comment: 14 page
Partition Functions of Pure Spinors
We compute partition functions describing multiplicities and charges of
massless and first massive string states of pure-spinor superstrings in
3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet
of minimal supersymmetry in d dimensions. At the first massive string level we
find a massive spin-two multiplet. The result is confirmed by a direct analysis
of the BRST cohomology at ghost number one. The central charges of the pure
spinor systems are derived in a manifestly SO(d) covariant way confirming that
the resulting string theories are critical. A critical string model with
N=(2,0) supersymmetry in d=2 is also described.Comment: LaTex, 30 p
Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom
We consider natural complex Hamiltonian systems with degrees of freedom
given by a Hamiltonian function which is a sum of the standard kinetic energy
and a homogeneous polynomial potential of degree . The well known
Morales-Ramis theorem gives the strongest known necessary conditions for the
Liouville integrability of such systems. It states that for each there
exists an explicitly known infinite set \scM_k\subset\Q such that if the
system is integrable, then all eigenvalues of the Hessian matrix V''(\vd)
calculated at a non-zero \vd\in\C^n satisfying V'(\vd)=\vd, belong to
\scM_k. The aim of this paper is, among others, to sharpen this result. Under
certain genericity assumption concerning we prove the following fact. For
each and there exists a finite set \scI_{n,k}\subset\scM_k such that
if the system is integrable, then all eigenvalues of the Hessian matrix
V''(\vd) belong to \scI_{n,k}. We give an algorithm which allows to find
sets \scI_{n,k}. We applied this results for the case and we found
all integrable potentials satisfying the genericity assumption. Among them
several are new and they are integrable in a highly non-trivial way. We found
three potentials for which the additional first integrals are of degree 4 and 6
with respect to the momenta.Comment: 54 pages, 1 figur
A note on supersymmetric D-brane dynamics
We study the spin dependence of D-brane dynamics in the Green-Schwarz
formalism of boundary states. In particular we show how to interpret insertion
of supercharges on the boundary state as sources of non-universal spin effects
in D-brane potentials. In this way we find for a generic (D)p-brane, potentials
going like corresponding to interactions between the
different components of the D-brane supermultiplet. From the eleven dimensional
point of view, these potentials arise from the exchange of field strengths
corresponding to the graviton and the three form, coupled non-minimally to the
branes. We show how an annulus computation truncated to its massless
contribution is enough to reproduce these next-to-leading effects, meaning in
particular that the one-loop (M)atrix theory effective action should encode all
the spin dependence of low-energy supergravity interactions.Comment: LaTex file, 12 pages, no figures, some corrections in last section
and references added; version to appear in Physics Letters
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