Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector
Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector
复制标题
费米子幽灵领域威滕明星产品的 Moyal 配方
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Theodore G. Erler
中科院分区：
文献类型：
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作者：
Theodore G. Erler
本文用非交换场论的语言对Witten开玻色子弦场论中的费米子幽灵扇区进行了重新刻划。特别是，根据help -th/0202087的方法，我们发现在Siegel规范中Witten的星积大致对应于Clifford代数的连续张量积，我们用这种语言表述了该理论的重要算子，特别是真空弦场论的动力学算子和描述不稳定D-25膜真空的BRST算子。我们发现在这个公式中BRST算子是奇异的。我们探索了星积的替代算子/Moyal表示，类似于bar和Matsuo在最近的工作中广泛发展的分割弦描述和离散Moyal基（help -th/0204260）。最后，我们讨论了形式主义中一些有趣的奇点，以及如何调节它们。
In this paper, we recast the fermionic ghost sector of Witten's open bosonic string field theory in the language of noncommutative field theory. In particular, following the methods of hep-th/0202087, we find that in Siegel gauge Witten's star product roughly corresponds to a continuous tensor product of Clifford Algebras, and we formulate important operators of the theory in this language, notably the kinetic operator of vacuum string field theory and the BRST operator describing the vacuum of the unstable D-25 brane. We find that the BRST operator is singular in this formulation. We explore alternative operator/Moyal representations of the star product analogous to the split string description and the discrete Moyal basis developed extensively in recent work by Bars and Matsuo (hep-th/0204260). Finally, we discuss some interesting singularities in the formalism and how they may be regulated.