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E. Onofri

Publications and source records attributed to E. Onofri.

22 records · Page 2Linked to original sources
arXiv1995

A numerical study of the RG equation for the deformed $O(3)$ nonlinear sigma model

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two dimensional target space (deformation of the $O(3)$ sigma model). In particular, our analysis shows that the so-called sausages define an attracting manifold in the $U(1)$-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association put forward in Nucl. Phys., B406 (1993) 521 between the so-called $SSM_ν$ field theory and a certain $U(1)$-symmetric, factorized scattering theory (FST).

hep-th↗
arXiv1995

RENORMALONS FROM EIGHT LOOP EXPANSION OF THE GLUON CONDENSATE IN LATTICE GAUGE THEORY,

We use a numerical method to obtain the weak coupling perturbative coefficients of local operators with lattice regularization. Such a method allows us to extend the perturbative expansions obtained so far by analytical Feynman diagrams calculations. In SU(3) lattice gauge theory in four dimensions we compute the first eight coefficients of the expectation value of the Wilson loop on the elementary plaquette which is related to the gluon condensate. The computed eight coefficients grow with the order much faster than predicted by the presence of the infrared renormalon associated to the dimension of the gluon condensate. However the renormalon behaviour for large order is quite well reproduced if one considers the expansion coefficients in a new coupling related to the lattice coupling by large perturbative corrections. This is expected since the lattice and continuum Lambda scales differ by almost two orders of magnitude.

hep-th↗
arXiv1994

Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_μ(x) \to \exp\{A_μ(x)/\sqrtβ\}$ into the Langevin algorithm and the observables and to perform the expansion in β^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (β^{-4}) which extends by one loop the previously known series.

hep-lat↗