Kaluza-Klein Supergravity
Kaluza-Klein Supergravity
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DOI：
10.1016/0370-1573(86)90163-8
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
M. Duff;B. Nilsson;C. Pope
中科院分区：
文献类型：
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作者：
M. Duff;B. Nilsson;C. Pope
评论文章往往分为两类：要么是无偏见的，全面的参考文献列表，包括关于该主题的每一篇论文;要么是有选择性的，关注作者认为重要的内容。第一种是公平的，但并不总是很有用：评论的目的之一应该是让感兴趣但忙碌的读者不必费力地阅读不相关的内容。在这篇关于卡鲁扎-克莱因超引力的评论中，我们选择了后一种方法，尽管有偏见的风险。因此，我们开始时先说明我们的偏见，我们还不知道超引力[1，2，3，4]是否是一个关于真实的世界的理论，也不知道真实的世界是否象卡鲁扎-克莱因理论[5，6，7]所要求的那样，有多于四维的空间。然而，我们在这一领域的研究使我们相信，实现超引力的唯一方法是通过卡鲁扎-克莱因，而唯一可行的卡鲁扎-克莱因理论就是超引力。这篇物理学报告的目的就是要为这一观点提供论据，在这个过程中，我们将发现一些有趣的线索，表明卡鲁扎-克莱因超引力甚至可能是现实的。我们从1.2节开始开始，简要介绍卡鲁扎-克莱因理论的发展及其最终与超引力的合并。关于这个问题的想法肯定已经改变了多年来，我们提出了批评的某些混乱和误解，弥漫在旧卡鲁扎-克莱因文学，其中一些坚持到今天。(For例如，未能要求额外维度的“自发”而不是“临时”紧致化。）卡鲁扎-克莱因把高维理论解释为四维理论的方法在1.3节中给出。作为这些思想的经典例子，我们将在1.4节从现代视角讨论卡鲁扎的原始五维模型。它不是一个现实的理论，也不是我们感兴趣的高维模型的典型。然而，它是历史的兴趣和足够简单，它承认一个相当完整的分析，其性质，至少在经典的水平。特别是，我们能够以封闭形式写出有效四维拉格朗日量的对称性，包括大质量态。新的特征是Kac-Moody型无限参数代数的出现[8]。在我们看来，最有吸引力的Kaluza-Klein理论是超对称理论。然而，即使在这里，专家意见也分为纯粹主义者和实用主义者，前者的指导原则是理论的数学一致性和优雅性，后者则寻求与低能现象学直接接触。在这方面有两个问题：宇宙常数问题和手征性问题[9]。在理想情况下，我们希望能够解释夸克和轻子的手征表象，以及宇宙常数非常小的事实，至少在我们所处的阶段是这样。但是，如果这些属性立即出现在树中，
Review articles tend to fall into two categories: either they are unbiased and comprehensive with a list of references including every paper on the subject; or else they are selective, focusing attention on what the authors think is important. The first kind is fair but not always very useful: one of the purposes of a review should be to spare the interested but busy reader the task of wading through the irrelevant. In this review of Kaluza—Klein supergravity we have chosen the latter course, albeit at the risk of bias. So we shall begin by stating our prejudices.We do not yet know whether supergravity [1, 2, 3, 4] is a theory of the real world, nor whether the real world has more than four dimensions as demanded by Kaluza—Klein theories [5, 6, 7]. However, our research in this area has convinced us that the only way to do supergravity is via Kaluza—Klein and that the only viable Kaluza—Klein theory is supergravity. The purpose of this Physics Report is to present the case for this point of view and in the process we shall find some intriguing hints that Kaluza—Klein supergravity may even be realistic. We begin in section 1.2 with a brief history of the development of Kaluza—Klein theories and their eventual merger with supergravity. Ideas on the subject have certainly changed over the years and we present a critique of certain confusions and misapprehensions which pervade the old Kaluza—Klein literature, some of which persist to the present day.(For example, failure to demand “spontaneous” as opposed to “ad hoc” compactification of the extra dimensions.) The Kaluza—Klein recipe for interpreting a higher-dimensional theory as a four-dimensional theory is given in section 1.3. As the classic example of these ideas we discuss in section 1.4 the original five-dimensional model of Kaluza [5] from a modern perspective. It is not a realistic theory, nor is it typical of the kind of higher-dimensional models we are interested in. Nevertheless, it is of historical interest and sufficiently simple that it admits a fairly complete analysis of its properties, at least at the classical level. In particular, one is able to write down in closed form the symmetries of the effective four-dimensional Lagrangian, including the massive states. The novel feature is the emergence of infinite parameter algebras of the Kac—Moody type [8]. In our opinion, the most attractive Kaluza—Klein theories are the supersymmetric ones. Even here, however, expert opinion is divided between the purists, whose guiding principles are the mathematical consistency and elegance of the theory, and the pragmatists who are seeking to make immediate contact with low-energy phenomenology. Two problems spring to mind in this respect: the cosmological constant problem and the chirality problem [9]. Ideally, we would like to explain the observed chiral representations of the quarks and leptons and the fact that the cosmological constant is very small, at least in the phase in which we live. However, should these properties appear immediately at the tree