99,856 research outputs found
Quantum geometry of 2d gravity coupled to unitary matter
We show that there exists a divergent correlation length in 2d quantum
gravity for the matter fields close to the critical point provided one uses the
invariant geodesic distance as the measure of distance. The corresponding
reparameterization invariant two-point functions satisfy all scaling relations
known from the ordinary theory of critical phenomena and the KPZ exponents are
determined by the power-like fall off of these two-point functions. The only
difference compared to flat space is the appearance of a dynamically generated
fractal dimension d_h in the scaling relations. We analyze numerically the
fractal properties of space-time for Ising and three-states Potts model coupled
to 2d dimensional quantum gravity using finite size scaling as well as small
distance scaling of invariant correlation functions. Our data are consistent
with d_h=4, but we cannot rule out completely the conjecture d_H =
-2\alpha_1/\alpha_{-1}, where \alpha_{-n} is the gravitational dressing
exponent of a spin-less primary field of conformal weight (n+1,n+1). We compute
the moments and the loop-length distribution function and show that the
fractal properties associated with these observables are identical, with good
accuracy, to the pure gravity case.Comment: LaTeX2e, 38 pages, 13 figures, 32 eps files, added one referenc
Renorm-group, Causality and Non-power Perturbation Expansion in QFT
The structure of the QFT expansion is studied in the framework of a new
"Invariant analytic" version of the perturbative QCD. Here, an invariant
(running) coupling is transformed
into a "--analytized" invariant coupling which, by constuction, is free of ghost singularities due to
incorporating some nonperturbative structures.
Meanwhile, the "analytized" perturbation expansion for an observable , in
contrast with the usual case, may contain specific functions , the "n-th power of analytized as a whole", instead
of . In other words, the pertubation series for , due to
analyticity imperative, may change its form turning into an {\it asymptotic
expansion \`a la Erd\'elyi over a nonpower set} .
We analyse sets of functions and discuss properties of
non-power expansion arising with their relations to feeble loop and scheme
dependence of observables.
The issue of ambiguity of the invariant analytization procedure and of
possible inconsistency of some of its versions with the RG structure is also
discussed.Comment: 12 pages, LaTeX To appear in Teor. Mat. Fizika 119 (1999) No.
QCD Factorization of Quasi Generalized Gluon Distributions
We study the factorization relations between quasi gluon GPDs and twist-2
GPDs. The perturbative coefficient functions are obtained at one-loop level.
They are free from any collinear- or I.R. divergences. Unlike the case of the
factorization of quasi quark GPDs at one-loop, we have to add ghost
contributions for the factorization of quasi gluon GPDs in order to obtain
gauge-invariant results. In general, operators will be mixed beyond tree-level.
Our work shows that the mixing pattern of the nonlocal operators in quasi gluon
GPDs is the same as local operators, i.e., the nonlocal operators considered
are mixed with gauge-invariant operators, BRST-variation operators and
operators involving EOM operator. The factorization relations are obtained for
all quasi gluon GPDs. Taking the forward limit, we also obtain the relations
between quasi gluon PDFs and twist-2 PDFs.Comment: 23 pages, 5 figures, published versio
Gluon Pseudo-Distributions at Short Distances: Forward Case
We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone z2 → 0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln(−z2)-dependence at short distances z2. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs
Gluon Pseudo-Distributions at Short Distances: Forward Case
We present the results that are necessary in the ongoing lattice calculations
of the gluon parton distribution functions (PDFs) within the pseudo-PDF
approach. We give a classification of possible two-gluon correlator functions
and identify those that contain the invariant amplitude determining the gluon
PDF in the light-cone limit. One-loop calculations have been
performed in the coordinate representation and in an explicitly gauge-invariant
form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources
of the -dependence at short distances . The UV terms cancel in
the reduced Ioffe-time distribution (ITD), and we obtain the matching relation
between the reduced ITD and the light-cone ITD. Using a kernel form, we get a
direct connection between lattice data for the reduced ITD and the normalized
gluon PDF. We also show that our results may be used for a rather
straightforward calculation of the one-loop matching relations for quasi-PDFs.Comment: 8 pages, 5 figures. Gluon-quark term adde
Gauge invariant bound state equations for quark-antiquark systems in QCD
Using gauge invariant quark Green's functions, defined with path-ordered
gluon field phase factors along polygonal lines, and functional relations among
them, two compatible bound state equations of the Dirac type are established
for quark-antiquark systems, each relative to the quark or to the antiquark of
the system. The kernels of the bound state equations are defined through a
series of Wilson loop averages along closed polygonal contours and their
functional derivatives on them. A sufficient criterion for spontaneous chiral
symmetry breaking is derived, relating the Goldstone boson wave function in the
zero total momentum limit with the scalar part of the gauge invariant quark
two-point Green's function.Comment: 25 pages, 2 figures; v2: comments and references adde
Two-point gauge invariant quark Green's functions with polygonal phase factor lines
Polygonal lines are used for the paths of the gluon field phase factors
entering in the definition of gauge invariant quark Green's functions. This
allows classification of the Green's functions according to the number of
segments the polygonal lines contain. Functional relations are established
between Green's functions with polygonal lines with different numbers of
segments. An integrodifferential equation is obtained for the quark two-point
Green's function with a path along a single straight line segment where the
kernels are represented by a series of Wilson loop averages along polygonal
contours. The equation is exactly and analytically solved in the case of
two-dimensional QCD in the large- limit. The solution displays generation
of an infinite number of dynamical quark masses accompanied with branch point
singularities that are stronger than simple poles. An approximation scheme,
based on the counting of functional derivatives of Wilson loops, is proposed
for the resolution of the equation in four dimensions.Comment: 6 pages, PDFLatex uses elsarticle class. Invited talk at the
Conference Light Cone: Relativistic Hadronic and Particle Physics, 10-15
December 2012, Delhi, Indi
N=4 Scattering Amplitudes and the Deformed Grassmannian
15 pagesSome time ago the general tree-level scattering amplitudes of N=4 Super Yang-Mills theory were expressed as certain Grassmannian contour integrals. These remarkable formulas allow to clearly expose the super-conformal, dual super-conformal, and Yangian symmetries of the amplitudes. Using ideas from integrability it was recently shown that the building blocks of the amplitudes permit a natural multi-parameter deformation. However, this approach had been criticized by the observation that it seemed impossible to reassemble the building blocks into Yangian-invariant deformed non-MHV amplitudes. In this note we demonstrate that the deformations may be succinctly summarized by a simple modification of the measure of the Grassmannian integrals, leading to a Yangian-invariant deformation of the general tree-level amplitudes. Interestingly, the deformed building-blocks appear as residues of poles in the spectral parameter planes. Given that the contour integrals also contain information on the amplitudes at loop-level, we expect the deformations to be useful there as well. In particular, applying meromorphicity arguments, they may be expected to regulate all notorious infrared divergences. We also point out relations to Gelfand hypergeometric functions and the quantum Knizhnik-Zamolodchikov equations.Peer reviewe
Relations between integrated correlators in Supersymmetric Yang--Mills Theory
Integrated correlation functions in supersymmetric
Yang--Mills theory with gauge group can be expressed in terms of the
localised partition function, , deformed by a mass . Two such
cases are and , which are modular invariant functions of the complex coupling
. While was recently written in terms of a
two-dimensional lattice sum for any and , has only
been evaluated up to order in a large- expansion in terms of modular
invariant functions with no known lattice sum realisation. Here we develop
methods for evaluating to any desired order in and finite
. We use this new data to constrain higher loop corrections to the stress
tensor correlator, and give evidence for several intriguing relations between
and to all orders in . We also give
evidence that the coefficients of the expansion of can be
written as lattice sums to all orders. Lastly, these large and finite
results are used to accurately estimate the integrated correlators at
finite and finite .Comment: 30 pages plus appendices, 8 figure
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