杂种优势（0，2）Gepner模型及其相关几何
Heterotic (0,2) Gepner Models and Related Geometries
摘要：
在为我的老师沃尔夫冈·库默尔（Wolfgang Kummer）的纪念卷《基本相互作用》（Fundamental Interactions）作贡献的悲伤时刻，我决定收集并扩展一些90年代中期未发表的笔记，当时我开始在维也纳建立一个弦论小组，由沃尔夫冈担任粒子物理小组的负责人。他的态度非常支持，最好的表达是他说，一个人应该让所有的花朵盛开。我希望这些说明将是有用的，特别是鉴于目前的新的兴趣，杂种优势模型的建设。这一贡献的内容是基于精确的CFT和几何技术之间的桥梁，是由简单的电流模块化不变量的轨道解释。在这种语言中重新制定Gepner结构后，我描述了杂种优势（0，2）模型的推广及其应用于Gepner型和Distler-Kachru模型之间的几何/CFT等价性，该模型由Blumenwald，Schimmrigk和Wisskirchen提出。我们分析了一系列的异常方程的解决方案，讨论镜像对称性的问题，并使用扩展庞加莱多项式的建设扩展到朗道-金兹伯格模型超出理性的CFTs的领域。在附录中，我们讨论了Gepner点环面orbifolds，这提供了进一步的关系，自由玻色子和自由费米子，以及简单的电流在N=2 SCFT和极小模型。
英文摘要：
On the sad occasion of contributing to the memorial volume ``Fundamental Interactions'' for my teacher Wolfgang Kummer I decided to recollect and extend some unpublished notes from the mid 90s when I started to build up a string theory group in Vienna under Wolfgang as head of the particle physics group. His extremely supportive attitude was best expressed by his saying that one should let all flowers flourish. I hope that these notes will be useful in particular in view of the current renewed interest in heterotic model building. The content of this contribution is based on the bridge between exact CFT and geometric techniques that is provided by the orbifold interpretation of simple current modular invariants. After reformulating the Gepner construction in this language I describe the generalization to heterotic (0,2) models and its application to the Geometry/CFT equivalence between Gepner-type and Distler-Kachru models that was proposed by Blumenhagen, Schimmrigk and Wisskirchen. We analyze a series of solutions to the anomaly equations, discuss the issue of mirror symmetry, and use the extended Poincaré polynomial to extend the construction to Landau-Ginzburg models beyond the realm of rational CFTs. In the appendix we discuss Gepner points in torus orbifolds, which provide further relations to free bosons and free fermions, as well as - simple currents in N=2 SCFTs and minimal models.
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