14 research outputs found
Evolution Equation for Generalized Parton Distributions
The extension of the method [arXiv:hep-ph/0503109] for solving the leading
order evolution equation for Generalized Parton Distributions (GPDs) is
presented. We obtain the solution of the evolution equation both for the flavor
nonsinglet quark GPD and singlet quark and gluon GPDs. The properties of the
solution and, in particular, the asymptotic form of GPDs in the small x and \xi
region are discussed.Comment: REVTeX4, 34 pages, 3 figure
Boundary Shape and Casimir Energy
Casimir energy changes are investigated for geometries obtained by small but
arbitrary deformations of a given geometry for which the vacuum energy is
already known for the massless scalar field. As a specific case, deformation of
a spherical shell is studied. From the deformation of the sphere we show that
the Casimir energy is a decreasing function of the surface to volume ratio. The
decreasing rate is higher for less smooth deformations.Comment: 12 page
Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
The influence of uniaxial small-scale anisotropy on the stability of the
scaling regimes and on the anomalous scaling of the structure functions of a
passive scalar advected by a Gaussian solenoidal velocity field with finite
correlation time is investigated by the field theoretic renormalization group
and operator product expansion within one-loop approximation. Possible scaling
regimes are found and classified in the plane of exponents ,
where characterizes the energy spectrum of the velocity field in the
inertial range , and is related to the
correlation time of the velocity field at the wave number which is scaled
as . It is shown that the presence of anisotropy does not disturb
the stability of the infrared fixed points of the renormalization group
equations which are directly related to the corresponding scaling regimes. The
influence of anisotropy on the anomalous scaling of the structure functions of
the passive scalar field is studied as a function of the fixed point value of
the parameter which represents the ratio of turnover time of scalar field
and velocity correlation time. It is shown that the corresponding one-loop
anomalous dimensions, which are the same (universal) for all particular models
with concrete value of in the isotropic case, are different (nonuniversal)
in the case with the presence of small-scale anisotropy and they are continuous
functions of the anisotropy parameters, as well as the parameter . The
dependence of the anomalous dimensions on the anisotropy parameters of two
special limits of the general model, namely, the rapid-change model and the
frozen velocity field model, are found when and ,
respectively.Comment: revtex, 25 pages, 37 figure
Spacetime Properties of ZZ D-Branes
We study the tachyon and the RR field sourced by the ZZ D-branes in
type 0 theories using three methods. We first use the mini-superspace
approximation of the closed string wave functions of the tachyon and the RR
scalar to probe these fields. These wave functions are then extended beyond the
mini-superspace approximation using mild assumptions which are motivated by the
properties of the corresponding wave functions in the mini-superspace limit.
These are then used to probe the tachyon and the RR field sourced. Finally we
study the space time fields sourced by the ZZ D-branes using the FZZT
brane as a probe. In all the three methods we find that the tension of the
ZZ brane is times the tension of the ZZ brane. The RR
charge of these branes is non-zero only for the case of both and odd,
in which case it is identical to the charge of the brane. As a
consistency check we also verify that the space time fields sourced by the
branes satisfy the corresponding equations of motion.Comment: 32 pages, 4 figures. Clarifications on the principal characterization
of ZZ branes added. Reference adde
Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence
The problem of anomalous scaling in magnetohydrodynamics turbulence is
considered within the framework of the kinematic approximation, in the presence
of a large-scale background magnetic field. The velocity field is Gaussian,
-correlated in time, and scales with a positive exponent .
Explicit inertial-range expressions for the magnetic correlation functions are
obtained; they are represented by superpositions of power laws with
non-universal amplitudes and universal (independent of the anisotropy and
forcing) anomalous exponents. The complete set of anomalous exponents for the
pair correlation function is found non-perturbatively, in any space dimension
, using the zero-mode technique. For higher-order correlation functions, the
anomalous exponents are calculated to using the renormalization group.
The exponents exhibit a hierarchy related to the degree of anisotropy; the
leading contributions to the even correlation functions are given by the
exponents from the isotropic shell, in agreement with the idea of restored
small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in
the odd correlation functions : the skewness factor is slowly decreasing going
down to small scales and higher odd dimensionless ratios (hyperskewness etc.)
dramatically increase, thus diverging in the limit.Comment: 25 pages Latex, 1 Figur
Anomalous scaling of a passive scalar in the presence of strong anisotropy
Field theoretic renormalization group and the operator product expansion are
applied to a model of a passive scalar field, advected by the Gaussian strongly
anisotropic velocity field. Inertial-range anomalous scaling behavior is
established, and explicit asymptotic expressions for the n-th order structure
functions of scalar field are obtained; they are represented by superpositions
of power laws with nonuniversal (dependent on the anisotropy parameters)
anomalous exponents. In the limit of vanishing anisotropy, the exponents are
associated with tensor composite operators built of the scalar gradients, and
exhibit a kind of hierarchy related to the degree of anisotropy: the less is
the rank, the less is the dimension and, consequently, the more important is
the contribution to the inertial-range behavior. The leading terms of the even
(odd) structure functions are given by the scalar (vector) operators. For the
finite anisotropy, the exponents cannot be associated with individual operators
(which are essentially ``mixed'' in renormalization), but the aforementioned
hierarchy survives for all the cases studied. The second-order structure
function is studied in more detail using the renormalization group and
zero-mode techniques.Comment: REVTEX file with EPS figure