论文标题
副作用，氯化和关键的偏僻理论
Parafermionization, bosonization, and critical parafermionic theories
论文作者
论文摘要
我们为一维晶格模型和田野理论制定了$ \ mathbb {z} _k $ -parafermionization/hobosonization方案，从晶格上的大概jordan-wigner转换开始，从晶格上延伸了$ k = 2 $ k = 2 $的lattice。 $ \ mathbb {z} _k $ -parafermionization使我们能够调查偏见链的关键理论，其基本自由度是偏见的，我们发现它们的批判性无法由任何现有的共同字段理论描述。这些偏执狂的低能批判理论的模块化转换被认为是非常规的，因为当$ k> 2 $ $ k> 2 $时，它们的分区在圆环上的作用与任何共形场理论的变化不同。分区功能的显式形式是通过开发的副词来获得的，对于一大批关键的$ \ Mathbb {z} _K $ -Parafermionic链，其操作员的内容与任何相结式旋转和统计范围内与任何波斯型或费赛模型都具有本质上的不同。我们还使用parafermionization来耗尽所有$ \ mathbb {z} _k $ -parafermionic最小模型，并补充了早期在费米子情况下的作品。
We formulate a $\mathbb{Z}_k$-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality at $k=2$. The $\mathbb{Z}_k$-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory when $k>2$. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical $\mathbb{Z}_k$-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the $\mathbb{Z}_k$-parafermionic minimal models, complementing earlier works on fermionic cases.
