99,856 research outputs found

    Quantum geometry of 2d gravity coupled to unitary matter

    Get PDF
    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

    Get PDF
    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 a(Q2/Λ2)=β1αs(Q2)/4πa(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi is transformed into a "Q2Q^2--analytized" invariant coupling aan(Q2/Λ2)A(x)a_{\rm an}(Q^2/\Lambda^2) \equiv {\cal A}(x) which, by constuction, is free of ghost singularities due to incorporating some nonperturbative structures. Meanwhile, the "analytized" perturbation expansion for an observable FF, in contrast with the usual case, may contain specific functions An(x)=[an(x)]an{\cal A}_n(x)= [a^n(x)]_{\rm an}, the "n-th power of a(x)a(x) analytized as a whole", instead of (A(x))n({\cal A}(x))^n. In other words, the pertubation series for F(x)F(x), due to analyticity imperative, may change its form turning into an {\it asymptotic expansion \`a la Erd\'elyi over a nonpower set} {An(x)}\{{\cal A}_n(x)\}. We analyse sets of functions {An(x)}\{{\cal A}_n(x)\} 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

    Full text link
    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

    Get PDF
    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

    Get PDF
    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 z20z^2 \to 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)\ln (-z^2)-dependence at short distances z2z^2. 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

    Full text link
    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

    Full text link
    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-NcN_c 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

    Get PDF
    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 N=4\mathcal{N}=4 Supersymmetric Yang--Mills Theory

    Full text link
    Integrated correlation functions in N=4\mathcal{N}=4 supersymmetric Yang--Mills theory with gauge group SU(N)SU(N) can be expressed in terms of the localised S4S^4 partition function, ZNZ_N, deformed by a mass mm. Two such cases are CN=(Imτ)2ττˉm2logZNm=0\mathcal{C}_N=(\text{Im} \tau)^2 \partial_\tau\partial_{\bar\tau} \partial_m^2\log Z_N\vert_{m=0} and HN=m4logZNm=0\mathcal{H}_N=\partial_m^4\log Z_N\vert_{m=0}, which are modular invariant functions of the complex coupling τ\tau. While CN\mathcal{C}_N was recently written in terms of a two-dimensional lattice sum for any NN and τ\tau, HN\mathcal{H}_N has only been evaluated up to order 1/N31/N^3 in a large-NN expansion in terms of modular invariant functions with no known lattice sum realisation. Here we develop methods for evaluating HN\mathcal{H}_N to any desired order in 1/N1/N and finite τ\tau. We use this new data to constrain higher loop corrections to the stress tensor correlator, and give evidence for several intriguing relations between HN\mathcal{H}_N and CN\mathcal{C}_N to all orders in 1/N1/N. We also give evidence that the coefficients of the 1/N1/N expansion of HN\mathcal{H}_N can be written as lattice sums to all orders. Lastly, these large NN and finite τ\tau results are used to accurately estimate the integrated correlators at finite NN and finite τ\tau.Comment: 30 pages plus appendices, 8 figure
    corecore