Bagger-Lambert Theory for General Lie Algebras
Bagger-Lambert Theory for General Lie Algebras
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DOI：
10.1088/1126-6708/2008/06/075
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
J. Gomis;G. Milanesi;J. Russo
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文献类型：
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作者：
J. Gomis;G. Milanesi;J. Russo
从任意半简单李代数出发，构造了具有洛伦兹双不变度量的3-代数的完全反对称结构常数f^{ABCD}。结构常数f^{ABCD}可以用来写出一个最大超共形三维理论，该理论包含了多个M2膜的预期自由度，包括由自由标量场和费米子场描述的“质心”模式。规范场扇形简化为三维BF项，这是规范对称理论的基础。我们评论了量子理论的统一性问题，这是有问题的，尽管相互作用的特定形式阻止了鬼场在任何费曼图的内线中运行。给其中一个标量场一个期望值，就会得到具有两个U(1)多重态的最大超对称三维杨-米尔斯拉格朗日量，其中一个是鬼态的，在g_YM处解耦。
We construct the totally antisymmetric structure constants f^{ABCD} of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the "center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large g_YM.