AI 中文总结
研究通过SCFT/VOA对应，从无希格斯的四维${\cal N}=2$拉格朗日SCFT生成强有限但非有理VOA的例子。通过组合分类任务，发现这类例子稀疏，包括自由向量多重态等，还构造研究了相关VOA并确认其性质。
AI 中文摘要
顶点算子代数（VOA）在数学和物理中都得到了充分研究。理解最好的一类是强有理VOA，其表示范畴行为良好，是一个模范张量范畴。更复杂的是强有限但非有理的VOA，其表示范畴不是半单的（是“对数的”），但保持良好结构性质。已知这类的例子很少，这可能阻碍了全面数学理论的发展。SCFT/VOA对应提供了生成更多例子的自然方法：强有限但非有理的VOA预计来自不允许希格斯分支真空模空间的四维${\cal N}=2$拉格朗日超共形场论（SCFT）。我们处理对所有此类“无希格斯”拉格朗日SCFT进行分类的组合任务。令人惊讶的是，这类集合相当稀疏。自由向量多重态及其离散规范是直接例子。相互作用的无希格斯理论包括一个SO/USp箭图的无限序列和三个零星例子。我们构造并研究了与两个零星例子相关的新型VOA，并确认它们确实是强有限且对数的。
英文摘要
Vertex operator algebras (VOAs) are well studied in both mathematics and physics. The best understood class is that of strongly rational VOAs, whose representation category is maximally well behaved: indeed, it is a modular tensor category. At the next level of complexity are strongly finite but non-rational VOAs. Their representation category is not semisimple (it is ``logarithmic''), but maintains nice structural properties. Only a few families of examples in this class are known, a fact that may have hindered the development of a comprehensive mathematical theory. The SCFT/VOA correspondence provides a natural way to generate more examples: strongly finite but non-rational VOAs are expected to arise from four-dimensional ${\cal N}=2$ Lagrangian superconformal field theories (SCFTs) that do not admit a Higgs branch moduli space of vacua. We tackle the combinatorial task of classifying all such ``Higgsless'' Lagrangian SCFTs. To our surprise, this set turns out to be rather sparse. Free vector multiplets and their discrete gaugings are immediate examples. The interacting Higgsless theories comprise one infinite sequence of SO/USp quivers and three sporadic examples. We construct and study the novel VOAs associated to two of the sporadic examples, and confirm that they are indeed strongly finite and logarithmic.
Comments57 pages, 11 tables, 10 figures
