标题： 在规范线性sigma模型中非阿贝尔统计的无解定理 显示英文标题

标题： A no-go theorem for nonabelionic statistics in gauged linear sigma-models

摘要： 在黎曼曲面上临界耦合的规范线性sigma模型产生自对偶场论，其经典真空由涡旋方程描述。 对于结构群为${\rm U}(r)$的局部模型，我们通过基底曲面$\Sigma$的对称积来描述涡旋模空间，我们假设该曲面是紧致的。 然后我们证明所有这些纤维化都诱导基本群的同构。 一个结果是，这类模型中多涡旋的模空间都有阿贝尔基本群。 我们将这一事实解释为关于通过这些规范sigma模型的超对称版本（通过A扭转拓扑化）的基态实现非阿贝尔子的无解定理。 此分析基于通过其经典模空间上的超对称量子力学对QFT进行半经典近似。 显示英文摘要

摘要： Gauged linear sigma-models at critical coupling on Riemann surfaces yield self-dual field theories, their classical vacua being described by the vortex equations. For local models with structure group ${\rm U}(r)$, we give a description of the vortex moduli spaces in terms of a fibration over symmetric products of the base surface $\Sigma$, which we assume to be compact. Then we show that all these fibrations induce isomorphisms of fundamental groups. A consequence is that all the moduli spaces of multivortices in this class of models have abelian fundamental groups. We give an interpretation of this fact as a no-go theorem for the realization of nonabelions through the ground states of a supersymmetric version (topological via an A-twist) of these gauged sigma-models. This analysis is based on a semi-classical approximation of the QFTs via supersymmetric quantum mechanics on their classical moduli spaces.