额外维存在性的理论探讨  

Exploring the existence of extra dimension(s)

作　　者：李田军[1] 刘玉孝[2] 吕宏[3] 卢建新[4] Tianjun Li;Yuxiao Liu;Hong LU;Jianxin Lu(Institute of Theoretical Physics,Chinese Academy of Sciences,BeIJing 100190,China;Institute of Theoretical Physics,Lanzhou University,Lanzhou 730000,China;Department of Physics,Tianjin University,Tianjin 300350,China;The Interdisciplinary Center for Theoretical Study,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学院理论物理研究所,北京100190 [2]兰州大学理论物理研究所,兰州730000 [3]天津大学物理系,天津300350 [4]中国科学技术大学交叉学科理论研究中心,合肥230026

出　　处：《科学通报》2018年第24期2499-2508,共10页Chinese Science Bulletin

基　　金：国家自然科学基金(11235010;11475238;11375075;11522541;11475024;11175269;11235003;11647601;11775212)资助

摘　　要：是否存在超出我们生活的4维时空的额外维度是一个有趣而重要的问题.本文从理论角度探讨这一问题,先讨论了早期引力与电磁相互作用统一的5维卡鲁扎-克莱茵(Kaluza-Klein,KK)-理论,然后介绍了超对称和超引力与额外维的关联,最后介绍了弦理论和M-理论,并解释为何超弦理论本身的完善要求存在一个时空维度最大可以是11维的M-理论.至少从经典层面上,额外维对超对称和超引力来说仅仅是一种选择,不是必须的.目前,除4维N=8超引力理论有可能是一个自洽的量子引力理论,其他4维和高维的超引力理论紫外都有问题,需要考虑新的物理自由度,对应的紫外完善理论很可能就是弦/M-理论.弦理论对额外维的要求有所不同,其微扰量子自洽性要求额外维必须存在.例如,对超弦理论,时空必须是10维的.如果弦/M-理论的确是描述物质和相互作用的基本理论,那额外维就一定存在,同时需要对额外的空间维度作紧致化,且其尺度必须小于目前的实验限制.本文也讨论了一些相关唯象大额外维理论.Whether there exists extra dimensions is an interesting and fundamental question. In this article, certain aspects of this have been explored theoretically. For this purpose, we first discuss the role of an extra dimension in the early unification of the classical Einstein gravity and electromagnetic interaction, namely the Kaluza-Klein （KK-） theory, and the issues we encounter in carrying this out. We then move to discuss the relationship between supersymmetry and extra dimension（s） and point out that there exist well-defined quantum theories without gravity in six dimensions such as （2, 0） superconformal theory and little string theories, the former is a local field theory but has no Lagrangian description while the latter are non- local non-gravitational string theories. We discuss also the similar issue for supergravities in diverse dimensions and point out that the largest number of supersymmetries with propagating gravity degrees of freedom is N=8 in four dimensions and the largest number of spacetime dimensions for supergravity is eleven. We would like to stress that extra dimensions in classical supersymmetric theories such as supergravities in diverse dimensions appear only as an option. When gravity is included, the four-dimensional N=8 supergravity appears to be the only one so far which has the potential to be a good quantum gravity theory in the usual field theory sense. All the rest are sure to be UV incomplete ones whose UV completions require the existence of an unified theory which is most likely to be the string/M-theory. In this sense, a quantum consistent theory containing gravity needs extra dimensions in general. Good examples include both bosonic strings and superstrings. For the former, we need the spacetime dimensions to be twenty six while for the latter we need spacetime dimensions to be ten such that the corresponding theories are quantum consistent at least perturbatively. So for these quantum consistent theories containing gravity, extra dimensions are no longer optional

关 键 词：额外维 Kaluza-Klein(KK)-理论 超对称及超引力 弦/M-理论 大额外维理论 

分 类 号：O41[理学—理论物理]