An asymptotic solution of large-N QCD

Marco Bochicchio

doi:10.1051/epjconf/20148000010

Abstract

We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic $S$-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic $S$-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the $LSZ$ reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-$N$ $QCD$, and in particular on any string solution.

Highlights

Solving QCD in ’t Hooft large-N limit [1] is a long-standing difficult problem
An asymptotic solution of this kind would replace QCD viewed as a theory of gluons and quarks, that are strongly coupled in the infrared in perturbation theory, with a theory of an infinite number of glueballs and mesons, that are weakly coupled at all scales in the large-N limit [1]
EPJ Web of Conferences paper, that we call the asymptotically-free bootstrap 1, by which we extend the asymptotic theorem to three- and multi-point correlators and S -matrix amplitudes, getting in this way an asymptotic solution of large-N QCD in a sense specified below

Summary

Introduction

Solving QCD in ’t Hooft large-N limit [1] is a long-standing difficult problem. An easier problem is to find a solution, not exact, but only asymptotic in the ultraviolet (UV). The asymptotic structure of two-point correlators of any spin has been explicitly characterized by the asymptotic theorem [3] reported below, in ’t Hooft limit of any large-N confining asymptotically-free gauge theory massless in perturbation theory, such as massless QCD (i.e. QCD with massless quarks). This paper is a short communication, detailed proofs will appear elsewhere

Asymptotically-free bootstrap for massless large-N QCD

Asymptotic effective action and S -matrix amplitudes

Conclusions and outlook