自对偶临界Z（N）自旋系统中的SLE：CFT预言
SLE in self-dual critical Z(N) spin systems: CFT predictions
摘要：
Schramm-Loewner演化（SLE）描述了二维统计系统中畴壁在相变时的连续极限。本文考虑自对偶Z（N）自旋模型在临界点的SLE。对于N=2和N=3，这些模型对应于Ising和三态Potts模型。当N>5时，临界自对偶Z（N）自旋模型在连续极限下用中心电荷c>=1的非极小共形场论描述。通过研究相应的手征代数的表示，我们证明了两个特殊的算子满足一个两级零矢量条件，当N>=4时，该条件提供了一个来自超对称电流作用的附加项.对于N= 2，3，这些算子对应于与SLE_{16/3}（伊辛模型）以及与SLE_{24/5}和SLE_{10/3}（三态波茨模型）相关联的边界条件改变算子。我们提出了Z（N）格点模型中界面的定义。这些接口的缩放限制，预计将描述在自对偶临界点和N>=4的SLE_{4(N+1)/(N+2)}和SLE_{4(N+2)/(N+1)}过程。
英文摘要：
The Schramm-Loewner evolution (SLE) describes the continuum limit of domain walls at phase transitions in two dimensional statistical systems. We consider here the SLEs in the self-dual Z(N) spin models at the critical point. For N=2 and N=3 these models correspond to the Ising and three-state Potts model. For N>5 the critical self-dual Z(N) spin models are described in the continuum limit by non-minimal conformal field theories with central charge c>=1. By studying the representations of the corresponding chiral algebra, we show that two particular operators satisfy a two level null vector condition which, for N>=4, presents an additional term coming from the extra symmetry currents action. For N=2,3 these operators correspond to the boundary conditions changing operators associated to the SLE_{16/3} (Ising model) and to the SLE_{24/5} and SLE_{10/3} (three-state Potts model). We suggest a definition of the interfaces within the Z(N) lattice models. The scaling limit of these interfaces is expected to be described at the self-dual critical point and for N>=4 by the SLE_{4(N+1)/(N+2)} and SLE_{4(N+2)/(N+1)} processes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
