共形关联子系统
Conformal correlator systems
- Institut de physique théorique, CEA, CNRS, Université Paris-Saclay（理论物理研究所，法国原子能和替代能源委员会，法国国家科学研究中心，巴黎萨克雷大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出共形关联子系统，以描述临界统计模型中非CFT的共形协变关联子，其N点函数由4点决定，并构造了满足单值性约束的实例。
AI中文摘要：
在统计模型的临界极限中，存在非局域关联子，它们具有共形协变性，但不属于共形场论。为了描述这类关联子，我们定义了共形关联子系统，其公理比CFT的公理更弱。因此，N点关联子由4点关联子决定，而非CFT中的3点关联子。在二维中，共形自旋可取任意复数值，导致关联子具有非平凡的单值性。我们证明了球面上的4点关联子和环面上的1点关联子满足非平凡的单值性约束。我们在自由玻色子理论和临界环模型中构造了具有阿贝尔单值性的关联子。
英文摘要：
In critical limits of statistical models, there exist non-local correlators that are conformally covariant without belonging to a conformal field theory. To describe such correlators, we define conformal correlator systems, whose axioms are weaker than those of CFT. As a result, $N$-point correlators are determined by $4$-point correlators, instead of $3$-point correlators in CFT. In two dimensions, conformal spins may take arbitrary complex values, leading to correlators with nontrivial monodromies. We show that sphere $4$-point correlators and torus $1$-point correlators obey nontrivial monodromy constraints. We construct correlators with abelian monodromies in free bosonic theories and in critical loop models.
