论文标题
非阿布莱安人和阿拉德·赫尔佐格猜想的一些堂兄弟
Non-Abelian Anyons and Some Cousins of the Arad-Herzog Conjecture
论文作者
论文摘要
很久以前，Arad和Herzog（AH）猜想，在有限的简单群体中，两个长度的共轭类别的产物大于一个是单个共轭类。我们讨论了这一猜想对2+1维离散量规理论中非亚伯人的含义。以这种方式思考还提出了有关有限简单组及其相关离散量规理论的密切相关的陈述。我们证明了这些陈述，并为其有效性提供了一些物理直觉。最后，我们解释说，非亚伯有限的简单量规组缺乏某些二元性，提供了对AH猜想的非平凡检查。
Long ago, Arad and Herzog (AH) conjectured that, in finite simple groups, the product of two conjugacy classes of length greater than one is never a single conjugacy class. We discuss implications of this conjecture for non-abelian anyons in 2+1-dimensional discrete gauge theories. Thinking in this way also suggests closely related statements about finite simple groups and their associated discrete gauge theories. We prove these statements and provide some physical intuition for their validity. Finally, we explain that the lack of certain dualities in theories with non-abelian finite simple gauge groups provides a non-trivial check of the AH conjecture.
