9,187 research outputs found
Integrability and conformal data of the dimer model
The central charge of the dimer model on the square lattice is still being
debated in the literature. In this paper, we provide evidence supporting the
consistency of a description. Using Lieb's transfer matrix and its
description in terms of the Temperley-Lieb algebra at , we
provide a new solution of the dimer model in terms of the model of critical
dense polymers on a tilted lattice and offer an understanding of the lattice
integrability of the dimer model. The dimer transfer matrix is analysed in the
scaling limit and the result for is expressed in terms of
fermions. Higher Virasoro modes are likewise constructed as limits of elements
of and are found to yield a realisation of the Virasoro algebra,
familiar from fermionic ghost systems. In this realisation, the dimer Fock
spaces are shown to decompose, as Virasoro modules, into direct sums of
Feigin-Fuchs modules, themselves exhibiting reducible yet indecomposable
structures. In the scaling limit, the eigenvalues of the lattice integrals of
motion are found to agree exactly with those of the conformal integrals
of motion. Consistent with the expression for obtained from
the transfer matrix, we also construct higher Virasoro modes with and
find that the dimer Fock space is completely reducible under their action.
However, the transfer matrix is found not to be a generating function for the
integrals of motion. Although this indicates that Lieb's transfer matrix
description is incompatible with the interpretation, it does not rule out
the existence of an alternative, compatible, transfer matrix description
of the dimer model.Comment: 54 pages. v2: minor correction
1/N_c Corrections to the Hadronic Matrix Elements of Q_6 and Q_8 in K --> pi pi Decays
We calculate long-distance contributions to the amplitudes A(K^0 --> pi pi,
I) induced by the gluon and the electroweak penguin operators Q_6 and Q_8,
respectively. We use the 1/N_c expansion within the effective chiral lagrangian
for pseudoscalar mesons. In addition, we adopt a modified prescription for the
identification of meson momenta in the chiral loop corrections in order to
achieve a consistent matching to the short-distance part. Our approach leads to
an explicit classification of the loop diagrams into non-factorizable and
factorizable, the scale dependence of the latter being absorbed in the
low-energy coefficients of the effective theory. Along these lines we calculate
the one-loop corrections to the O(p^0) term in the chiral expansion of both
operators. In the numerical results, we obtain moderate corrections to
B_6^(1/2) and a substantial reduction of B_8^(3/2).Comment: 32 pages, LaTeX, 8 eps figures. One reference added, to appear in
Phys. Rev.
Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
We find the Hamiltonian for physical excitations of the classical bosonic
string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained
in a so-called uniform gauge which is related to the static gauge by a 2d
duality transformation. The Hamiltonian is of the Nambu type and depends on two
parameters: a single S^5 angular momentum J and the string tension \lambda. In
the general case both parameters can be finite. The space of string states
consists of short and long strings. In the sector of short strings the large J
expansion with \lambda'=\lambda/J^2 fixed recovers the plane-wave Hamiltonian
and higher-order corrections recently studied in the literature. In the strong
coupling limit \lambda\to \infty, J fixed, the energy of short strings scales
as \sqrt[4]{\lambda} while the energy of long strings scales as \sqrt{\lambda}.
We further show that the gauge-fixed Hamiltonian is integrable by constructing
the corresponding Lax representation. We discuss some general properties of the
monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum
perfectly agrees with the one obtained earlier for some specific cases.Comment: 30 pages, LaTex; v2: a few comments added, misprints corrected,
references adde
Scalar perturbations in regular two-component bouncing cosmologies
We consider a two-component regular cosmology bouncing from contraction to
expansion, where, in order to include both scalar fields and perfect fluids as
particular cases, the dominant component is allowed to have an intrinsic
isocurvature mode. We show that the spectrum of the growing mode of the Bardeen
potential in the pre-bounce is never transferred to the dominant mode of the
post-bounce. The latter acquires at most a dominant isocurvature component,
depending on the relative properties of the two fluids. Our results imply that
several claims in the literature need substantial revision.Comment: 10 pages, 1 figur
Recent Progress in AdS/CFT
The study of AdS/CFT (or gauge/gravity) duality has been one of the most
active and illuminating areas of research in string theory over the past
decade. The scope of its relevance and the insights it is providing seem to be
ever expanding. In this talk I briefly describe some of the attempts to explore
how the duality works for maximally supersymmetric systems.Comment: 11 page
Cutoff-independent regularization of four-fermion interactions for color superconductivity
We implement a cutoff-independent regularization of four-fermion interactions
to calculate the color-superconducting gap parameter in quark matter. The
traditional cutoff regularization has difficulties for chemical potentials \mu
of the order of the cutoff \Lambda, predicting in particular a vanishing gap at
\mu \sim \Lambda. The proposed cutoff-independent regularization predicts a
finite gap at high densities and indicates a smooth matching with the weak
coupling QCD prediction for the gap at asymptotically high densities.Comment: 5 pages, 1 eps figure - Revised manuscript to match the published
pape
Spectral method for matching exterior and interior elliptic problems
A spectral method is described for solving coupled elliptic problems on an
interior and an exterior domain. The method is formulated and tested on the
two-dimensional interior Poisson and exterior Laplace problems, whose solutions
and their normal derivatives are required to be continuous across the
interface. A complete basis of homogeneous solutions for the interior and
exterior regions, corresponding to all possible Dirichlet boundary values at
the interface, are calculated in a preprocessing step. This basis is used to
construct the influence matrix which serves to transform the coupled boundary
conditions into conditions on the interior problem. Chebyshev approximations
are used to represent both the interior solutions and the boundary values. A
standard Chebyshev spectral method is used to calculate the interior solutions.
The exterior harmonic solutions are calculated as the convolution of the
free-space Green's function with a surface density; this surface density is
itself the solution to an integral equation which has an analytic solution when
the boundary values are given as a Chebyshev expansion. Properties of Chebyshev
approximations insure that the basis of exterior harmonic functions represents
the external near-boundary solutions uniformly. The method is tested by
calculating the electrostatic potential resulting from charge distributions in
a rectangle. The resulting influence matrix is well-conditioned and solutions
converge exponentially as the resolution is increased. The generalization of
this approach to three-dimensional problems is discussed, in particular the
magnetohydrodynamic equations in a finite cylindrical domain surrounded by a
vacuum
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