Eur. Phys. J. C (2009) 61: 69-73
https://doi.org/10.1140/epjc/s10052-009-1008-0

Regular Article - Theoretical Physics

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

¹ Department of Physics and Astronomy, Theoretical Physics II, University of Bochum, 150 Universitätsstrasse, 44780, Bochum, Germany
² V.A. Fock Department of Theoretical Physics, St. Petersburg State University, 1 ul. Ulyanovskaya, 198504, St. Petersburg, Russia

^* e-mail: afonin24@mail.ru

Received: 16 June 2008
Revised: 14 January 2009
Published online: 26 March 2009

Abstract

The AdS/QCD models suggest the 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 parameterization of the non-perturbative dynamics of strong interactions, we discuss on a qualitative level an alternative possibility for a simpler 5-dimensional parameterization of the main phenomena in the low-energy QCD. We propose to interpret the effect of chiral symmetry breaking as the effective appearance of a compactified extra dimension with the radius of the order of the 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 us 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.