285 research outputs found
Geometric Lagrangians for massive higher-spin fields
Lagrangians for massive, unconstrained, higher-spin bosons and fermions are
proposed. The idea is to modify the geometric, gauge invariant Lagrangians
describing the corresponding massless theories by the addition of suitable
quadratic polynomials. These polynomials provide generalisations of the
Fierz-Pauli mass term containing all possible traces of the basic field. No
auxiliary fields are needed.Comment: 50 pages, 3 appendices; typos corrected, comments and references
added. To appear in Nucl. Phys.
Asymptotic wave-splitting in anisotropic linear acoustics
Linear acoustic wave-splitting is an often used tool in describing sound-wave
propagation through earth's subsurface. Earth's subsurface is in general
anisotropic due to the presence of water-filled porous rocks. Due to the
complexity and the implicitness of the wave-splitting solutions in anisotropic
media, wave-splitting in seismic experiments is often modeled as isotropic.
With the present paper, we have derived a simple wave-splitting procedure for
an instantaneously reacting anisotropic media that includes spatial variation
in depth, yielding both a traditional (approximate) and a `true amplitude'
wave-field decomposition. One of the main advantages of the method presented
here is that it gives an explicit asymptotic representation of the linear
acoustic-admittance operator to all orders of smoothness for the smooth,
positive definite anisotropic material parameters considered here. Once the
admittance operator is known we obtain an explicit asymptotic wave-splitting
solution.Comment: 20 page
Geometry and dynamics of higher-spin frame fields
We give a systematic account of unconstrained free bosonic higher-spin fields
on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism.
The generalized spin connections are determined by solving a chain of
torsion-like constraints. Via a generalization of the vielbein postulate these
allow to determine higher-spin Christoffel symbols, whose relation to the de
Wit--Freedman connections is discussed. We prove that the generalized Einstein
equations, despite being of higher-derivative order, give rise to the AdS
Fronsdal equations in the compensator formulation. To this end we derive
Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the
possibility of a geometrical and local action principle, which is manifestly
invariant under unconstrained higher-spin symmetries.Comment: 30 pages, uses youngtab.sty, v2: minor changes, references adde
The Generalized Dirichlet to Neumann map for the KdV equation on the half-line
For the two versions of the KdV equation on the positive half-line an
initial-boundary value problem is well posed if one prescribes an initial
condition plus either one boundary condition if and have the
same sign (KdVI) or two boundary conditions if and have
opposite sign (KdVII). Constructing the generalized Dirichlet to Neumann map
for the above problems means characterizing the unknown boundary values in
terms of the given initial and boundary conditions. For example, if
and are given for the KdVI
and KdVII equations, respectively, then one must construct the unknown boundary
values and , respectively. We
show that this can be achieved without solving for by analysing a
certain ``global relation'' which couples the given initial and boundary
conditions with the unknown boundary values, as well as with the function
, where satisifies the -part of the associated
Lax pair evaluated at . Indeed, by employing a Gelfand--Levitan--Marchenko
triangular representation for , the global relation can be solved
\emph{explicitly} for the unknown boundary values in terms of the given initial
and boundary conditions and the function . This yields the unknown
boundary values in terms of a nonlinear Volterra integral equation.Comment: 21 pages, 3 figure
An action variable of the sine-Gordon model
It was conjectured that the classical bosonic string in AdS times a sphere
has a special action variable which corresponds to the length of the operator
on the field theory side. We discuss the analogous action variable in the
sine-Gordon model. We explain the relation between this action variable and the
Backlund transformations and show that the corresponding hidden symmetry acts
on breathers by shifting their phase. It can be considered a nonlinear analogue
of splitting the solution of the free field equations into the positive- and
negative-frequency part.Comment: v3,4: added explanations, discussion of O(N) sigma-model in section 5
v5: correction in the Introduction, small change
Matching Higher Conserved Charges for Strings and Spins
We demonstrate that the recently found agreement between one-loop scaling
dimensions of large dimension operators in N=4 gauge theory and energies of
spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite
number of hidden higher commuting charges. This dynamical agreement is of a
mathematically highly intricate and non-trivial nature. In particular, on the
gauge side the generating function for the commuting charges is obtained by
integrable quantum spin chain techniques from the thermodynamic density
distribution function of Bethe roots. On the string side the generating
function, containing information to arbitrary loop order, is constructed by
solving exactly the Backlund equations of the integrable classical string sigma
model. Our finding should be an important step towards matching the integrable
structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof
that the entire infinite towers of commuting gauge and string charges match);
references adde
Local non-equilibrium distribution of charge carriers in a phase-coherent conductor
We use the scattering matrix approach to derive generalized Bardeen-like
formulae for the conductances between the contacts of a phase-coherent
multiprobe conductor and a tunneling tip which probes its surface. These
conductances are proportional to local partial densities of states, called
injectivities and emissivities. The current and the current fluctuations
measured at the tip are related to an effective local non-equilibrium
distribution function. This distribution function contains the
quantum-mechanical phase-coherence of the charge carriers in the conductor and
is given as products of injectivities and the Fermi distribution functions in
the electron reservoirs. The results are illustrated for measurements on
ballistic conductors with barriers and for diffusive conductors.Comment: 4 pages, 2 figures, submitted to "Comptes Rendus de l'Academie des
Sciences
On the Integrability of large N Plane-Wave Matrix Theory
We show the three-loop integrability of large N plane-wave matrix theory in a
subsector of states comprised of two complex light scalar fields. This is done
by diagonalizing the theory's Hamiltonian in perturbation theory and taking the
large N limit. At one-loop level the result is known to be equal to the
Heisenberg spin-1/2 chain, which is a well-known integrable system. Here,
integrability implies the existence of hidden conserved charges and results in
a degeneracy of parity pairs in the spectrum. In order to confirm integrability
at higher loops, we show that this degeneracy is not lifted and that
(corrected) conserved charges exist. Plane-wave matrix theory is intricately
connected to N=4 Super Yang-Mills, as it arises as a consistent reduction of
the gauge theory on a three-sphere. We find that after appropriately
renormalizing the mass parameter of the plane-wave matrix theory the effective
Hamiltonian is identical to the dilatation operator of N=4 Super Yang-Mills
theory in the considered subsector. Our results therefore represent a strong
support for the conjectured three-loop integrability of planar N=4 SYM and are
in disagreement with a recent dual string theory finding. Finally, we study the
stability of the large N integrability against nonsupersymmetric deformations
of the model.Comment: 20 pages, 1 figur
A dual lagrangian for non-Abelian tensor gauge fields
For non-Abelian tensor gauge fields of the lower rank we have found an
alternative expression for the field strength tensors, which transform
homogeneously with respect to the complementary gauge transformations and allow
us to construct the dual Lagrangian.Comment: 13 pages, LaTex fil
Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background
We study a string motion in the Lunin-Maldacena background, that is, the
\beta-deformed AdS_5 \times \tilde{S}^5 background dual to a \beta-deformation
of \mathcal{N} = 4 super Yang-Mills theory. For real \beta we construct a
rotating and wound string solution which has two unequal spins in \tilde{S}^5.
The string energy is expressed in terms of the spins, the winding numbers and
the deformation parameter. In the expansion of \lambda/J^2 with the total spin
J and the string tension \sqrt{\lambda} we present ``one-loop" and ``two-loop"
energy corrections. The ``one-loop" one agrees with the one-loop anomalous
dimension of the corresponding gauge-theory scalar operators obtained in
hep-th/0503192 from the \beta-deformed Bethe equation as well as the
anisotropic Landau-Lifshitz equation.Comment: 13 pages, LaTeX, no figure
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