临界回路模型中的对角场
Diagonal fields in critical loop models
摘要：
在临界环模型中，存在任意共形维数的对角场，其$3$点函数与刘维理论在$c\leq 1$的点函数一致。我们研究了它们的$N$ -点函数，它依赖于球面上组合不等价环的$2^{N-1}$权，该环具有$N$穿孔.使用数值共形引导方法，我们发现，$4$ -点函数分解成无穷的，但离散的线性组合的共形块。我们的结论是对角场属于$O(n)$模型的扩展。
英文摘要：
In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose $3$-point functions coincide with those of Liouville theory at $c\leq 1$. We study their $N$-point functions, which depend on the $2^{N-1}$ weights of combinatorially inequivalent loops on a sphere with $N$ punctures. Using a numerical conformal bootstrap approach, we find that $4$-point functions decompose into infinite but discrete linear combinations of conformal blocks. We conclude that diagonal fields belong to an extension of the $O(n)$ model.
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