论文标题
二维O（N）模型和对数CFTS
Two-dimensional O(n) models and logarithmic CFTs
论文作者
论文摘要
我们研究O（n） - 对称二维形成型场理论（CFTS），其连续n范围低于两个。这些CFT描述了自我避免循环的固定点行为。有一对已知的固定点通过RG流量连接。当n等于两个，这对应于kosterlitz-无尽的临界理论时，固定点会发生碰撞。我们发现，对于n，这些CFT是对数，并且包含负规范状态。特别是，o（n）电流属于交错的对数倍数。使用共形性引导方法，我们追踪负规范状态在n = 2时如何将单位性恢复。 IR固定点具有局部相关的操作员，在CFT的所有已知全局对称性下，Singlet，但是，可以通过RG流动而无需调整即可到达。此外，我们在密切相关的POTTS模型中观察到对数相关器。
We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG flow. When n is equal to two, which corresponds to the Kosterlitz-Thouless critical theory, the fixed points collide. We find that for n generic these CFTs are logarithmic and contain negative norm states; in particular, the O(n) currents belong to a staggered logarithmic multiplet. Using a conformal bootstrap approach we trace how the negative norm states decouple at n = 2, restoring unitarity. The IR fixed point possesses a local relevant operator, singlet under all known global symmetries of the CFT, and, nevertheless, it can be reached by an RG flow without tuning. Besides, we observe logarithmic correlators in the closely related Potts model.
