VOA与二维SCFT的补充注释
Supplementary Notes on VOA and 2D SCFT
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中文总结 AI 辅助
本文以顶点算子代数语言补充二维共形场论细节，提出利用两个辅助参数表述Ramond扇区交叉对称性，并系统推广至满足四条件的简单流扩张类。
中文摘要 AI 辅助
本注释的第2至3节主要为作者私人使用而编写，旨在以顶点算子代数（VOA）的语言组织二维（一般非全纯）共形场论（CFT）中的材料，并收集其中的微妙细节。主题的选择旨在补充该主题的入门物理教科书。第4节以顶点算子超代数（SVOA）的语言处理（一般非全纯）Type 0 CFT。利用两个辅助参数，给出了Ramond（SVOA扭曲）扇区[分别对应Ramond-Ramond扇区]中态的交错超算符[分别对应CFT顶点超算符]的交叉对称性和表述。该表述允许系统推广到由四个条件表征的简单流扩张类：（1）第三上同调消失，（2）斜对称双乘性形式，（3）简单流的无不动点作用，以及（4）正文中描述的另一个附加条件。
英文摘要
Sections 2--3 of this note were prepared primarily for the author's private use, as a means of organizing the materials in (generally non-holomorphic) conformal field theory (CFT) on 2-dimensions in the language of the vertex operator algebra, and also of collecting subtle details. The choice of topics is intended to supplement introductory physics textbooks on the subject. Section 4 deals with (generally non-holomorphic) Type 0 CFTs in the language of vertex operator superalgebra (SVOA). Formulations of crossing symmetry and intertwining superoperators [resp. CFT vertex superoperators] of states in the Ramond (SVOA-twisted) sector [resp. the Ramond--Ramond sector] are presented by using two auxiliary parameters. The formulation allows systematic generalization to the class of simple current extensions characterized by four conditions: (1) the vanishing third cohomology, (2) skew-symmetric bimultiplicative form, (3) fixed-point-free action of simple currents, and (4) one additional condition described in the main text.
发表机构
- Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo（东京大学宇宙物理数学研究所）
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