论文标题
将两个初次和中央电荷的统一RCFT分类小于25
Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
论文作者
论文摘要
我们将所有二维，统一的，理性的共同场理论与两个初次分类，中央指控$ C <25 $和任意的Wronskian指数。在数学列表中，我们将所有强烈的常规顶点操作员代数（VOAS）分类为中央电荷$ C <25 $和两个简单的模块。我们发现，任何这样的理论都是Mathur-Mukhi-sen（MMS）理论之一$ \ Mathsf {a} _ {1,1} $，$ \ Mathsf {g} _ {2,1} $，$ \ Mathsf {f}通过这样的MMS理论，手性代数的固定剂量是一个主要操作员（也称为Holomorthic VOA）。通过利用有关全体形态VOA分类的现有结果，我们能够明确列举上述所有cosets并计算其角色。这导致了123种理论，其中大多数是新的。我们强调，我们的工作是对RCFT的真正分类，而不仅仅是角色的。我们的技术是一般的，我们认为它们提供了一种有前途的策略，可以将中央电荷低的手性代数分类超过两个初选。
We classify all two-dimensional, unitary, rational conformal field theories with two primaries, central charge $c<25$, and arbitrary Wronskian index. In mathematical parlance, we classify all strongly regular vertex operator algebras (VOAs) with central charge $c<25$ and exactly two simple modules. We find that any such theory is either one of the Mathur-Mukhi-Sen (MMS) theories $\mathsf{A}_{1,1}$, $\mathsf{G}_{2,1}$, $\mathsf{F}_{4,1}$, or $\mathsf{E}_{7,1}$, or it is a coset of a chiral algebra with one primary operator (also known as a holomorphic VOA) by such an MMS theory. By leveraging existing results on the classification of holomorphic VOAs, we are able to explicitly enumerate all of the aforementioned cosets and compute their characters. This leads to 123 theories, most of which are new. We emphasize that our work is a bona fide classification of RCFTs, not just of characters. Our techniques are general, and we argue that they offer a promising strategy for classifying chiral algebras with low central charge beyond two primaries.
