Two-dimensional sigma models: Modelling non-perturbative effects in quantum chromodynamics
Two-dimensional sigma models: Modelling non-perturbative effects in quantum chromodynamics
复制标题
二维西格玛模型：量子色动力学中的非微扰效应建模
DOI：
10.1016/0370-1573(84)90021-8
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
V. Zakharov
中科院分区：
文献类型：
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作者：
V. Novikov;M. Shifman;A. Vainshtein;V. Zakharov
本文讨论了四维规范理论与二维sigma模型之间存在的平行关系。我们使用sigma模型作为实验室，允许我们研究诸如算子积扩展超越微扰理论，真空凝聚，低能定理和其他非微扰方面的问题。所有这些问题都在当前的文献中进行了深入的讨论，我们对这种情况进行了批判性的分析。特别地，它解释了，与最近的主张相反，人们可以用一种完全一致的方式来定义超越微扰理论的算子乘积展开，没有歧义。文章的第二部分详细讨论了超对称的O(3) sigma模型。在对模型作了简单的描述之后，我们把注意力集中在瞬子上。描述了基于实例的精确计算gel - mann - low函数和双离子凝聚体的方法。我们以前在四维杨-米尔斯理论中使用过类似的方法。在这里，我们试图在简化的条件下阐明该方法的各个方面。其基本点是：(i)从纯经典分析得到的瞬时测度；（ii）自对偶外域的非重整化定理；(3)真空凝聚体的存在及其与超对称的相容性。出于教学目的，我们在技术细节和计算上使用了大量的空间。
This review is devoted to the discussion of the parallel existing between four-dimensional gauge theories and two-dimensional sigma models. We use sigma models as a laboratory allowing us to investigate such issues as the operator product expansion beyond perturbation theory, vacuum condensates, low-energy theorems and other non-perturbative aspects. All these questions are intensively discussed in the current literature, and we give a critical analysis of the situation. In particular, it is explained that, contrary to recent claims, one can define the operator product expansion beyond perturbation theory in a perfectly consistent way, with no ambiguities.The second part of the review represents a detailed discussion of the supersymmetric O(3) sigma model. After a simple description of the model we concentrate on instantons. The instanton-based method for calculating the exact Gell-Mann-Low function and bifermionic condensates is described. An analogue of this method has been previously used by us in four-dimensional Yang-Mills theories. Here we try to elucidate all aspects of the method in simplified conditions. The basic points are: (i) the instanton measure from purely classical analysis; (ii) a non-renormalization theorem in self-dual external fields; (iii) existence of vacuum condensates and their compatibility with supersymmetry.Pursuing pedagogical purposes we use much space for technical details and computations.