The relaxed three-algebras: their matrix representation and implications for multi M2-brane theory
The relaxed three-algebras: their matrix representation and implications for multi M2-brane theory
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DOI：
10.1088/1126-6708/2008/12/037
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发表时间：
2008-07
影响因子：
5.4
通讯作者：
M. Ali-Akbari;M. Sheikh-Jabbari;J. Simón
中科院分区：
文献类型：
--
作者：
M. Ali-Akbari;M. Sheikh-Jabbari;J. Simón
我们认为可以放宽最近用于构造D = 3 N = 8超共形场论的非结合三代数的要求，并引入“松弛三代数”的概念.我们提出了一个具体的实现的放松三代数的经典李代数的矩阵表示，赋予一个非结合的四括号结构，这是规定取代三代数的三括号。我们表明，无论是基于so（4）的解决方案，以及与非正定度量的情况下，找到一个统一的描述在我们的设置。我们讨论了我们的四括号表示的含义D = 3，N = 8和多M2-膜理论，并表明我们的设置可以揭示的问题的负动能自由度的洛伦兹情况。
We argue that one can relax the requirements of the non-associative threealgebras recently used in constructing D = 3 N = 8 superconformal field theories, and introduce the notion of “relaxed three-algebras”. We present a specific realization of the relaxed three-algebras in terms of classical Lie algebras with a matrix representation, endowed with a non-associative four-bracket structure which is prescribed to replace the three-brackets of the three-algebras. We show that both the so(4)-based solutions as well as the cases with non-positive definite metric find a uniform description in our setting. We discuss the implications of our four-bracket representation for the D = 3, N = 8 and multi M2-brane theory and show that our setup can shed light on the problem of negative kinetic energy degrees of freedom of the Lorentzian case.