标题： 非阿贝尔任意子和阿拉德-赫尔佐格猜想的一些变体 显示英文标题

标题： Non-Abelian Anyons and Some Cousins of the Arad-Herzog Conjecture

摘要： 很久以前，Arad 和 Herzog（AH）猜想，在有限单群中，两个长度大于一的共轭类的乘积永远不会是一个单独的共轭类。 我们讨论这个猜想对2+1维离散规范理论中的非阿贝尔任意子的影响。 以这种方式思考也提出了关于有限单群及其相关离散规范理论的密切相关的陈述。 我们证明了这些陈述，并提供了一些它们有效性的物理直觉。 最后，我们解释了具有非阿贝尔有限单群规范的理论中缺乏某些对偶性，为AH猜想提供了非平凡的验证。 显示英文摘要

摘要： 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.