QCD and dimensional deconstruction

Abstract

Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an ``open moose.'' Such a model has a large number K of hidden gauge groups as well as a global chiral symmetry. In the continuum limit $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\infty}$ the model becomes a 4+1 dimensional theory of a gauge field propagating in a dilaton background and an external space-time metric with two boundaries. We show that the model reproduces several well known phenomenological and theoretical aspects of low-energy hadron dynamics, such as vector meson dominance. We derive the general formulas for the mass spectrum, the decay constants of the pion and vector mesons, and the couplings between mesons. We then consider two simple realizations, one with a flat metric and another with a ``cosh'' metric interpolating between two anti--de Sitter (AdS) boundaries. For the pion form factor, the single pole \ensuremath{\rho}-meson dominance is exact in the latter case and approximate in the former case. We discover that an AdS/conformal field theory-like prescription emerges in the computation of current-current correlators. We speculate on the role of the model in the theory dual to QCD.