An asymptotic solution of large-$N$ $QCD$

TL;DR

This paper develops an asymptotic solution for correlators and S-matrix amplitudes in large-$N$ QCD, using a new field-theoretical technique called the asymptotically-free bootstrap, which aligns with perturbative results in the ultraviolet.

Contribution

It introduces the asymptotically-free bootstrap method, providing a novel approach to solving large-$N$ QCD correlators and S-matrix in the asymptotic regime.

Findings

Provides asymptotic expressions for correlators and S-matrix in large-$N$ QCD.

Shows the S-matrix depends only on the particle spectrum, not anomalous dimensions.

Sets strong constraints on possible solutions of large-$N$ QCD, including string models.

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.