Operator Algebras and Conformal Field Theory
Operator Algebras and Conformal Field Theory
复制标题
DOI：
--
复制
发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Jϋrg Frόhlich
中科院分区：
文献类型：
--
作者：
Jϋrg Frόhlich
我们用代数场论的方法定义和研究了二维手征共形场论。我们首先通过表征真空部门的这种理论，并表明，在非常一般的假设下，他们的代数的局部可观同构的独特的超有限型III 1因子。证明了由局部可观量代数确定的共形网满足Haag对偶。在共形场论的真空扇区上的莫比乌斯群的表示（可能是整个Virasoro代数的表示）由与其真空态和共形网相关的Tomita-Takesaki模算子唯一确定。然后，我们开发的理论Moebius协变表示的共形网，使用的方法Doplicer，哈格和罗伯茨。我们应用我们的结果的表示理论的循环群。我们的分析是出于希望找到一个“背景独立”的共形场理论制定。
We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satisfy Haag duality. The representation of the Moebius group (and presumably of the entire Virasoro algebra) on the vacuum sector of a conformal field theory is uniquely determined by the Tomita-Takesaki modular operators associated with its vacuum state and its conformal net. We then develop the theory of Moebius covariant representations of a conformal net, using methods of Doplicher, Haag and Roberts. We apply our results to the representation theory of loop groups. Our analysis is motivated by the desire to find a "background-independent" formulation of conformal field theories.