CHROMOGRAVITY: QCD-INDUCED DIFFEOMORPHISMS

Abstract

We expand the QCD gluon field [Formula: see text] around a constant “pure gauge” solution [Formula: see text] in the IR sector, i.e. [Formula: see text] and provide a mathematical definition for an “IR limit” in which the frequencies of the fluctuating field [Formula: see text] vanish. We prove that in this limit, SU (3) color gauge transformations become equivalent to space-time diffeomorphisms. A gravity-like contribution is then shown to emerge from the overall “n-gluon exchange” component in the expansion of the generating functional of QCD Green functions, with the two-gluon term acting like the metric field in gravity. This QCD-induced “chromogravity” provides an effective long range action, i.e. longer-ranged than the contribution of quark-antiquark (meson) exchanges. We conjecture chromogravity to be responsible for many of the features of the hadron spectrum and of color confinement, issues for which there is as yet no proof in QCD (including lattice calculations), beyond general qualitative arguments. The method exhibits a smooth transition to the perturbative and semiperturbative treatment of high energy hadron scattering, including the emergence of the Pomeranchuk trajectory.