About the possibility of five-dimensional effective theories for low-energy QCD

Abstract

The AdS/QCD models suggest an interesting idea that the effective theory of low-energy QCD may be formulated as a 5-dimensional field theory in the weak coupling regime in which the fifth coordinate plays a role of inverse energy scale. Taking the point of view that this is just an efficient parametrization of the non-perturbative dynamics of strong interactions, we discuss on a qualitative level an alternative possibility for a simpler 5-dimensional parametrization of main phenomena in the low-energy QCD. We propose to interpret the effect of chiral symmetry breaking as an effective appearance of compactified extra dimension with the radius of the order of inverse scale of chiral symmetry breaking. Following some heuristic arguments two dual scenarios for the emergence of the excited light mesons are introduced: In the first scenario, the meson resonances are interpreted as the effects of Kaluza-Klein excitations of quarks inside mesons, in the second one, as the formation of gluon strings wound around the compactified dimension an appropriate number of times. Matching of these scenarios permits to express the slope of radial Regge trajectories through the order parameters of the chiral symmetry breaking, with the compactification radius being excluded. This example shows qualitatively that the extra dimension may play an auxiliary role providing a short way for deriving new relations.