282 research outputs found
Evaluating the AdS dual of the critical O(N) vector model
We argue that the AdS dual of the three dimensional critical O(N) vector
model can be evaluated using the Legendre transform that relates the generating
functionals of the free UV and the interacting IR fixed points of the boundary
theory. As an example, we use our proposal to evaluate the minimal bulk action
of the scalar field that it is dual to the spin-zero ``current'' of the O(N)
vector model. We find that the cubic bulk self interaction coupling vanishes.
We briefly discuss the implications of our results for higher spin theories and
comment on the bulk-boundary duality for subleading N.Comment: 17 pages, 1 figure, v2 references added, JHEP versio
Rational three-spin string duals and non-anomalous finite size effects
We determine by a one line computation the one-loop conformal dimension and
the associated non-anomalous finite size correction for all operators dual to
spinning strings of rational type having three angular momenta (J_1,J_2,J_3) on
S^5. Finite size corrections are conjectured to encode information about string
sigma model loop corrections to the spectrum of type IIB superstrings on
AdS_5xS^5. We compare our result to the zero-mode contribution to the leading
quantum string correction derived for the stable three-spin string with two out
of the three spin labels identical and observe agreement. As a side result we
clarify the relation between the Bethe root description of three-spin strings
of the type (J,J',J') with respectively J>J' and J<J'.Comment: 15 pages, v2: comparison to string theory changed, references added,
v3: textual modifications and title change
Role of phason-defects on the conductance of a 1-d quasicrystal
We have studied the influence of a particular kind of phason-defect on the
Landauer resistance of a Fibonacci chain. Depending on parameters, we sometimes
find the resistance to decrease upon introduction of defect or temperature, a
behavior that also appears in real quasicrystalline materials. We demonstrate
essential differences between a standard tight-binding model and a full
continuous model. In the continuous case, we study the conductance in relation
to the underlying chaotic map and its invariant. Close to conducting points,
where the invariant vanishes, and in the majority of cases studied, the
resistance is found to decrease upon introduction of a defect. Subtle
interference effects between a sudden phason-change in the structure and the
phase of the wavefunction are also found, and these give rise to resistive
behaviors that produce exceedingly simple and regular patterns.Comment: 12 pages, special macros jnl.tex,reforder.tex, eqnorder.tex. arXiv
admin note: original tex thoroughly broken, figures missing. Modified so that
tex compiles, original renamed .tex.orig in source
On the Non-invasive Measurement of the Intrinsic Quantum Hall Effect
With a model calculation, we demonstrate that a non-invasive measurement of
intrinsic quantum Hall effect defined by the local chemical potential in a
ballistic quantum wire can be achieved with the aid of a pair of voltage leads
which are separated by potential barriers from the wire. B\"uttiker's formula
is used to determine the chemical potential being measured and is shown to
reduce exactly to the local chemical potential in the limit of strong potential
confinement in the voltage leads. Conditions for quantisation of Hall
resistance and measuring local chemical potential are given.Comment: 16 pages LaTex, 2 post-script figures available on reques
Scattering in flatland: Efficient representations via wave atoms
This paper presents a numerical compression strategy for the boundary
integral equation of acoustic scattering in two dimensions. These equations
have oscillatory kernels that we represent in a basis of wave atoms, and
compress by thresholding the small coefficients to zero. This phenomenon was
perhaps first observed in 1993 by Bradie, Coifman, and Grossman, in the context
of local Fourier bases \cite{BCG}. Their results have since then been extended
in various ways. The purpose of this paper is to bridge a theoretical gap and
prove that a well-chosen fixed expansion, the nonstandard wave atom form,
provides a compression of the acoustic single and double layer potentials with
wave number as -by- matrices with
nonnegligible entries, with a constant that depends on the relative
accuracy \eps in an acceptable way. The argument assumes smooth, separated,
and not necessarily convex scatterers in two dimensions. The essential features
of wave atoms that enable to write this result as a theorem is a sharp
time-frequency localization that wavelet packets do not obey, and a parabolic
scaling wavelength (essential diameter). Numerical experiments
support the estimate and show that this wave atom representation may be of
interest for applications where the same scattering problem needs to be solved
for many boundary conditions, for example, the computation of radar cross
sections.Comment: 39 page
Finite-Size Corrections to Anomalous Dimensions in N=4 SYM Theory
The scaling dimensions of large operators in N=4 supersymmetric Yang-Mills
theory are dual to energies of semiclassical strings in AdS(5)xS(5). At one
loop, the dimensions of large operators can be computed with the help of Bethe
ansatz and can be directly compared to the string energies. We study
finite-size corrections for Bethe states which should describe quantum
corrections to energies of extended semiclassical strings.Comment: 10 page
Semiclassical Strings on AdS_5 x S^5/Z_M and Operators in Orbifold Field Theories
We show agreements, at one-loop level of field theory, between energies of
semiclassical string states on AdS_5 x S^5/Z_M and anomalous dimensions of
operators in N=0,1,2 orbifold field theories originating from N=4 SYM. On field
theory side, one-loop anomalous dimension matrices can be regarded as
Hamiltonians of spin chains with twisted boundary conditions. These are
solvable by Bethe ansatz. On string side, twisted sectors emerge and we obtain
some string configurations in twisted sectors. In SU(2) subsectors, we compare
anomalous dimensions with string energies and see agreements. We also see
agreements between sigma models of both sides in SU(2) and SU(3) subsectors.Comment: LaTeX, 23 pages, 4 figures; v2 minor corrections, added references;
v3 typos corrected, published versio
On the pulsating strings in AdS_5 x T^{1,1}
We study the class of pulsating strings in AdS_5 x T^{1,1}. Using a
generalized ansatz for pulsating string configurations we find new solutions of
this class. Further we semiclassically quantize the theory and obtain the first
correction to the energy. The latter, due to AdS/CFT correspondence, is
supposed to give the anomalous dimensions of operators in the dual N=1
superconformal gauge field theory.Comment: 12 pages, improvements made, references adde
Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
From the SU(2) spin chain sigma model at the one-loop and two-loop orders we
recover the classical circular string solution with two S^5 spins (J_1, J_2) in
the AdS_5 x S^5 string theory. In the SL(2) sector of the one-loop spin chain
sigma model we explicitly construct a solution which corresponds to the folded
string solution with one AdS_5 spin S and one S^5 spin J. In the one-loop
general sigma model we demonstrate that there exists a solution which
reproduces the energy of the circular constant-radii string solution with three
spins (S_1, S_2, J).Comment: 16 pages, LaTeX, no figure
Classical/quantum integrability in non-compact sector of AdS/CFT
We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory
and compare their integrable structures. We formulate and solve the
Riemann-Hilbert problem for the finite gap solutions of the classical sigma
model and show that at one loop it is identical to the classical limit of Bethe
equations of the spin (-1/2) chain for the dilatation operator of SYM.Comment: 27 pages, 1 figure; v2: unphysical windings around the time direction
eliminated; v3: dicsussion of finite-size corrections remove
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