Generalized Weinberg Sum Rules in Deconstructed QCD

Recently, Son and Stephanov have considered an "open moose" as a possibledual model of a QCD-like theory of chiral symmetry breaking. In this note wedemonstrate that although the Weinberg sum rules are satisfied in any suchmodel, the relevant sums converge very slowly and in a manner unlike QCD.Further, we show that such a model satisfies a set of generalized sum rules.These sum rules can be understood by looking at the operator product expansionfor the correlation function of chiral currents, and correspond to the absenceof low-dimension gauge-invariant chiral symmetry breaking condensates. Theseresults imply that, regardless of the couplings and F-constants chosen, theopen moose is not the dual of any QCD-like theory of chiral symmetry breaking.We also show that the generalized sum rules can be "solved", leading to acompact expression for the difference of vector- and axial-current correlationfunctions. This expression allows for a simple formula for the S parameter(L_10), which implies that S is always positive and of order one in any(unitary) open linear moose model. Therefore the S parameter is positive andorder one in any "Higgsless model" based on the continuum limit of a linearmoose regardless of the warping or position-dependent gauge-coupling chosen.Comment: 12 pages, 5 eps figures; reference to overlapping work adde