arXiv 0802.04792008-02-04hep-th

高自旋规范对称性的统一结构

Towards Unifying Structures in Higher Spin Gauge Symmetry

Anders K. H. Bengtsson

备注：: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
发表信息：: SIGMA 4:013,2008
DOI：: 10.3842/SIGMA.2008.013

摘要：

这篇文章是简要的性质，概述了许多仍然不完全理解的高自旋场论的一些特点。我们主要考虑高自旋规范场本身作为独立的理论结构，而不是它们作为另一个系统的一部分出现的情况。考虑到在更高自旋规范场之间引入相互作用的问题，历史上有两条广泛的途径。一种方法需要测量一个非阿贝尔全局对称代数，在这个过程中使其局部化。另一种方法需要变形一个已经局部但阿贝尔的规范代数，在这个过程中使它成为非阿贝尔的。在两种途径都被探索过的情况下，例如自旋为1和2的规范场，结果与杨-米尔斯理论和爱因斯坦引力一致（除了概念和技术问题）。在无限高自旋规范场塔的情况下，M. Vasiliev，而第二种方法，在沉睡了很长一段时间后，最近又受到了几位作者的新关注。在本文中，我们简要地回顾了一些方面的历史，更高的自旋规范场的背景下，试图比较规范与变形的方法。一个共同的统一结构的强同伦李代数的基础上这两种方法将被讨论。现代变形的方法，使用BRST-BV方法，将被描述，因为它是目前开发的。第一个步骤的制定在分类语言的操作将被概述。一些方面的问题，似乎没有得到彻底调查指出。

英文摘要：

This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical constructs and not circumstances where they occur as part of another system. Considering the problem of introducing interactions among higher spin gauge fields, there has historically been two broad avenues of approach. One approach entails gauging a non-Abelian global symmetry algebra, in the process making it local. The other approach entails deforming an already local but Abelian gauge algebra, in the process making it non-Abelian. In cases where both avenues have been explored, such as for spin 1 and 2 gauge fields, the results agree (barring conceptual and technical issues) with Yang-Mills theory and Einstein gravity. In the case of an infinite tower of higher spin gauge fields, the first approach has been thoroughly developed and explored by M. Vasiliev, whereas the second approach, after having lain dormant for a long time, has received new attention by several authors lately. In the present paper we briefly review some aspects of the history of higher spin gauge fields as a backdrop to an attempt at comparing the gauging vs. deforming approaches. A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. The modern deformation approach, using BRST-BV methods, will be described as far as it is developed at the present time. The first steps of a formulation in the categorical language of operads will be outlined. A few aspects of the subject that seems not to have been thoroughly investigated are pointed out.

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摘要：

英文摘要：

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