Axiomatic Conformal Field Theory
Axiomatic Conformal Field Theory
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DOI：
10.1007/s002200050031
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发表时间：
1998-10
影响因子：
2.4
通讯作者：
M. Gaberdiel;P. Goddard
中科院分区：
文献类型：
--
作者：
M. Gaberdiel;P. Goddard
本文提出了一种新的严格的共形场论方法。基本对象是复值振幅族，它定义了亚纯共形场论（或手征代数），并自然地导致拓扑向量空间的定义，其中顶点算子作为连续算子。事实上，为了发展理论，莫比乌斯不变性，而不是完全的共形不变性是必需的，但它表明，每一个莫比乌斯理论可以扩展到共形理论的Virasoro场的建设。在这种方法中，共形场论的表示自然定义在一个家庭的振幅与适当的分析性质。结果表明，这些振幅也可以来自一个合适的亚纯理论中的状态的集合。朱的代数，然后自然出现的代数条件的国家定义最高的重量表示必须满足。朱氏代数的表示与最高权表示的分类之间的关系得到了解释。
A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, Möbius invariance rather than full conformal invariance is required but it is shown that every Möbius theory can be extended to a conformal theory by the construction of a Virasoro field.In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained.