Generalized Weinberg sum rules in deconstructed QCD
Generalized Weinberg sum rules in deconstructed QCD
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DOI：
10.1088/1126-6708/2004/06/004
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发表时间：
2004-03
影响因子：
5.4
通讯作者：
R. Chivukula;M. Kurachi;M. Tanabashi
中科院分区：
文献类型：
--
作者：
R. Chivukula;M. Kurachi;M. Tanabashi
最近，Son和Stephanov考虑了一个“开放的驼鹿”作为手征对称性破缺的类QCD理论的一个可能的对偶模型。在本文中，我们证明了，虽然温伯格求和规则是满足任何这样的模型，有关的总和收敛非常缓慢，并在一种方式不同于QCD。此外，我们证明了这样的模型满足一组广义求和规则。这些求和规则可以通过观察手征流的相关函数的算符乘积展开来理解，并且对应于低维规范不变的手征对称性破缺凝聚的缺乏。这些结果意味着，无论耦合和F常数的选择，开放驼鹿是不是任何手征对称性破缺的QCD类理论的对偶。我们还表明，广义和规则可以“解决”，导致一个紧凑的表达矢量和轴向电流相关函数的差异。这个表达式允许S参数（L10）的简单公式，这意味着S总是正的，并且在任何（酉）开放线性驼鹿模型中是一阶的。因此，S参数是正的，并且在任何基于线性驼鹿的连续极限的“无希格斯模型”中是一阶的，而不管选择的是翘曲还是位置相关的规范耦合。
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 (L10), 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.