Polynomial equations for rational conformal field theories
Polynomial equations for rational conformal field theories
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DOI：
10.1016/0370-2693(88)91796-0
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发表时间：
1988-10
影响因子：
4.4
通讯作者：
G. Moore;N. Seiberg
中科院分区：
文献类型：
--
作者：
G. Moore;N. Seiberg
有理共形场论的共形块的对偶性定义了可用于构造理论中所有一元性和模变换的表示的矩阵。这些对偶矩阵满足有限数量的独立多项式方程，这意味着对有理共形场论中允许的单项性的约束。这些方程包括证明 Verlinde 最近的猜想所需的关键恒等式，即单循环模变换 S 对角化融合规则。使用这种形式，我们证明了 g=0 四点函数的对偶性和所有单循环单点函数的模不变性保证了所有阶的模不变性。对偶矩阵方程在共形场论的分类中应该很有用。
Duality of the conformal blocks of a rational conformal field theory defines matrices which may be used to construct representations of all monodromies and modular transformations in the theory. These duality matrices satisfy a finite number of independent polynomial equations, which imply constraints on monodromies allowed in rational conformal field theories. The equations include a key identity needed to prove a recent conjecture of Verlinde that the one-loop modular transformation S diagonalizes the fusion rules. Using this formalism we show that duality of the g=0 four-point function and modular invariance of all one-loop one-point functions guarantee modular invariance to all orders. The equations for duality matrices should be useful in the classification of conformal field theories.