High orders perturbation theory and dual models for Yang-Mills theories

Abstract

We start with the QCD sum rules which are originally based on the idea that it is the power-like corrections to the parton model which are related to the confinement. The naive use of the Operator Product Expansion ensures that there is a 'gap' in the powers of ${\Lambda }_{QCD}$ which miss the quadratic terms and start with the quartic term, proportional to the gluon condensate, $<(G_{\mu \nu }^a{)}^2>$. We review how this hypothesis stood against various checks through the last three decades and how it was modified through inclusion of the missing link, that is quadratic corrections. In field theoretic language the quadratic corrections are dual to long perturbative series. In the dual description, the quadratic corrections are conveniently parameterized in terms of the metric in extra dimensions. We emphasize that the dual models do not incorporate the so called infrared renormalon.

arXiv commentTalk at the Conference QCD10, Montpellier, July 2010

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Cited by in corpus (6)

• Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory
• Compelling evidence of renormalons in QCD from high order perturbative expansions
• Wilson loops to 20th order numerical stochastic perturbation theory
• Model of the N-Quark Potential in SU(N) Gauge Theory using Gauge-String Duality
• Some Properties of the $QQq$-Quark Potential in String Models
• The static quark self-energy at large orders from NSPT