Chromogravity - An Effective Diff(4,R) Gauge for the IR region of QCD

Abstract

Previous work on the IR regime approximation of QCD in which the dominant contribution comes from a dressed two-gluon effective metric-like field $G_{\mu \nu }=g_{ab}{A}_{\mu }^a{A}_{\nu }^b$ ($g_{ab}$ a color SU(3) metric) is reviewed. The QCD gauge is approximated by effective "chromodiffeomorphisms", i.e. by a gauge theory based on a pseudo-diffeomorphisms group. The second-quantized $G_{\mu \nu }$ field, together with the Lorentz generators close on the $\overline{SL}(4,R)$ algebra. This algebra represents a spectrum generating algebra for the set of hadron states of a given flavor - hadronic "manifields" transforming w.r.t. $\overline{SL}(4,R)$ (infinite-dimensional) unitary irreducible representations. The equations of motion for the effective pseudo-gravity are derived from a quadratic action describing Riemannian pseudo-gravity in the presence of shear ($\overline{SL}(4,R)$ covariant) hadronic matter currents. These equations yield $p^{-4}$ propagators, i.e. a linearly rising confining potential $H(r)\sim r$, as well as linear $J\sim m^2$ Regge trajectories. The $\overline{SL}(4,R)$ symmetry based dynamical theory for the QCD IR region is successfully applied to hadron resonances. The pseudo-gravity potential reaches over to Nuclear Physics, where its $J^P=2^{+},0^{+}$ quanta provide for the ground state excitations of the Arima-Iachello Interacting Boson Model.