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Register a new userAsymptotic behavior of large polygonal Wilson loops in confining gauge theories
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P. V. Pobylitsa
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In the framework of effective string theory (EST), the asymptotic behavior of a large Wilson loop in confining gauge theories can be expressed via Laplace determinant with Dirichlet boundary condition on the Wilson contour. For a general polygonal region, Laplace determinant can be computed using the conformal anomaly and Schwarz-Christoffel transformation. One can construct ratios of polygonal Wilson loops whose large-size limit can be expressed via computable Laplace determinants and is independent of the (confining) gauge group. These ratios are computed for hexagon polygons both in EST and by Monte Carlo (MC) lattice simulations for the tree-dimensional lattice Z2 gauge theory (dual to Ising model) near its critical point. For large hexagon Wilson loops a perfect agreement is observed between the asymptotic EST expressions and the lattice MC results.
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The asymptotic behavior of Wilson loops in the large-size limit ($Lrightarrowinfty$) in confining gauge theories with area law is controlled by effective string theory (EST). The $L^{-2}$ term of the large-size expansion for the logarithm of Wilson loop appears within EST as a two-loop correction. Ultraviolet divergences of this two-loop correction for polygonal contours can be renormalized using an analytical regularization constructed in terms of Schwarz-Christoffel mapping. In the case of triangular Wilson loops this method leads to a simple final expression for the $L^{-2}$ term.
We propose and discuss a new approach to the analysis of the correlation functions which contain light-like Wilson lines or loops, the latter being cusped in addition. The objects of interest are therefore the light-like Wilson null-polygons, the soft factors of the parton distribution and fragmentation functions, high-energy scattering amplitudes in the eikonal approximation, gravitational Wilson lines, etc. Our method is based on a generalization of the universal quantum dynamical principle by J. Schwinger and allows one to take care of extra singularities emerging due to light-like or semi-light-like cusps. We show that such Wilson loops obey a differential equation which connects the area variations and renormalization group behavior of those objects and discuss the possible relation between geometrical structure of the loop space and area evolution of the light-like cusped Wilson loops.
The behaviour of the space-like string tension in the high temperature phase is studied. Data obtained in the $Z_2$ gauge model in (2+1) dimensions are compared with predictions of a simple model of a fluctuating flux tube with finite thickness. It is shown that in the high temperature phase contributions coming from the fluctuations of the flux tube vanish. As a consequence we also show that in (2+1) dimensional gauge theories the thickness of the flux tube coincides with the inverse of the deconfinement temperature.
We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than 2 particles in quantum field theories. To deal with $n$-particles in the center of mass flame coherently, we introduce the Jacob coordinates of $n$ particles and then combine their $3(n-1)$ coordinates into the one spherical coordinate in $D=3(n-1)$ dimensions. We parametrize on-shell $T$-matrix for $n$-particle system of scalar fields at low energy, using the unitarity constraint of the $S$-matrix. We then express asymptotic behaviors of the NBS wave function for $n$ particles at low energy, in terms of parameters of $T$-matrix, and show that the NBS wave function carry the information of $T$-matrix such as phase shifts and mixing angles of the $n$-particle system in its own asymptotic behavior, so that the NBS wave function can be considered as the scattering wave of $n$-particles in quantum mechanics. This property is one of the essential ingredients of the HAL QCD scheme to define potential from the NBS wave function in quantum field theories such as QCD. Our results, together with an extension to systems with spin 1/2 particles, justify the HAL QCDs definition of potentials for 3 or more nucleons(baryons) in terms the NBS wave functions.
We study the asymptotic behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop values are consistent with those extracted from previous perturbative studies of the gluon propagator. However the effective $Lambda_{ms}$ scale which reproduces the data does depend strongly upon the order of perturbation theory and on the renormalization scheme used in the parametrization. We show how the truncation of the perturbative series can account for the magnitude of the dependency in this energy range. The contribution of non-perturbative corrections will be discussed elsewhere.
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