Constraints on conformal field theories in diverse dimensions from the bootstrap mechanism.
Constraints on conformal field theories in diverse dimensions from the bootstrap mechanism.
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自举机制对不同维度共形场论的约束。
DOI：
10.1103/physrevlett.111.161602
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发表时间：
2013
影响因子：
8.6
通讯作者：
F. Gliozzi
中科院分区：
文献类型：
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作者：
F. Gliozzi
最近，人们发展了一种有效的数值方法来实现不同时空维共形场理论的算符维度和算符乘积展开系数的交叉对称性和酉性约束。似乎只能对位于允许参数空间边界的理论进行计算。这里指出，只要我们知道低位主算符集的融合代数，类似的方法就可以应用于更大类的共形场论，无论是否酉性，并且不存在自由参数。作为一个例子，我们使用第一原理，在没有唯象输入的情况下，计算了三维和四维空间中与杨-李边缘奇异性相关的局域算符的最低标度维。边缘指数与最新的数值估计值相比是有利的。并在三维临界伊辛模型上对该方法进行了一致性检验。
Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and operator product expansion coefficients of conformal field theories in diverse space-time dimensions. It appears that the calculations can be done only for theories lying at the boundary of the allowed parameter space. Here it is pointed out that a similar method can be applied to a larger class of conformal field theories, whether unitary or not, and no free parameter remains, provided we know the fusion algebra of the low lying primary operators. As an example we calculate using first principles, with no phenomenological input, the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity in three and four space dimensions. The edge exponents compare favorably with the latest numerical estimates. A consistency check of this approach on the 3D critical Ising model is also made.