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arXiv 0807.1570hep-th
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松弛三代数的矩阵表示及其对多M2-brane理论的意义

Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory

M. Ali-Akbari, M. M. Sheikh-Jabbari, J. Simon

摘要:

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。

英文摘要:

We argue that one can relax the requirements of the non-associative three-algebras 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.

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