标题： 交叉环态和二维伊辛场理论的对偶性 显示英文标题

标题： Crosscap states and duality of Ising field theory in two dimensions

摘要： 我们为二维（2D）伊辛场理论提出了两种不同的交叉帽态。 这两种交叉帽态在对径点上识别伊辛自旋或对偶自旋（域壁），被证明通过克朗默斯-瓦纳尔对偶变换相关联。 我们推导了它们的马约拉纳自由场表示，并扩展了玻色化技术以计算具有不同交叉帽边界条件的二维伊辛共形场理论（CFT）的相关函数。 我们进一步发展了一种共形微扰理论，以计算克莱因瓶熵作为二维伊辛场理论中的普遍标度函数 [Phys. Rev. Lett. 130, 151602 (2023)]。 本工作中开发的形式适用于许多其他受相关算符扰动的二维CFT。 显示英文摘要

摘要： We propose two distinct crosscap states for the two-dimensional (2D) Ising field theory. These two crosscap states, identifying Ising spins or dual spins (domain walls) at antipodal points, are shown to be related via the Kramers-Wannier duality transformation. We derive their Majorana free field representations and extend bosonization techniques to calculate correlation functions of the 2D Ising conformal field theory (CFT) with different crosscap boundaries. We further develop a conformal perturbation theory to calculate the Klein bottle entropy as a universal scaling function [Phys. Rev. Lett. 130, 151602 (2023)] in the 2D Ising field theory. The formalism developed in this work is applicable to many other 2D CFTs perturbed by relevant operators.