Generalized Weinberg Sum Rules in Deconstructed QCD

Abstract

Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, 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 expansion for the correlation function of chiral currents, and correspond to the absence of low-dimension gauge-invariant chiral symmetry breaking condensates. These results imply that, regardless of the couplings and F-constants chosen, the open 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 a compact expression for the difference of vector- and axial-current correlation functions. 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 and order one in any "Higgsless model" based on the continuum limit of a linear moose regardless of the warping or position-dependent gauge-coupling chosen.

12 pages, 5 eps figures; reference to overlapping work added

References in corpus (5)

• QCD and dimensional deconstruction
• Weakly coupled Higgsless theories and precision electroweak tests
• Oblique Corrections from Higgsless Models in Warped Space
• Higgsless Electroweak Symmetry Breaking from Theory Space
• The role of spurions in Higgs-less electroweak effective theories

Cited by in corpus (11)

• The Structure of Corrections to Electroweak Interactions in Higgsless Models
• Moose models with vanishing $S$ parameter
• Consistent high-energy constraints in the anomalous QCD sector
• Dropping rho and A_1 Meson Masses at Chiral Phase Transition in the Generalized Hidden Local Symmetry
• (Not) Summing over Kaluza-Kleins
• Holography, chiral Lagrangian and form factor relations
• Multi-Gauge-Boson Vertices and Chiral Lagrangian Parameters in Higgsless Models with Ideal Fermion Delocalization
• Topcolor breaking through boundary conditions
• (Reverse) Engineering Vacuum Alignment
• On the Evaluation of Gluon Condensate Effects in the Holographic Approach to QCD
• Locality in Theory Space