arXiv 1503.005262015-03math-phmath.MP

规范线性西格玛模型中非交换统计量的一个No-go定理

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

Indranil Biswas, Nuno M. Romão

备注：: Final version; to appear in Adv. Theo. Math. Phys
发表信息：: Adv. Theor. Math. Phys. 21 (2017) 901-920

摘要：

规范线性西格玛模型在临界耦合黎曼表面产生自对偶场论，其经典真空被描述的涡旋方程。对于具有结构群${\rm U}(r)$的局部模型，我们给出了涡模空间在基表面$Σ$的对称乘积上的纤维化的描述，我们假设它是紧的。然后，我们表明，所有这些纤维诱导基本群的同构。一个推论是这类模型中所有多顶点的模空间都有交换基本群。我们给出了一个解释，这一事实作为一个不去定理实现nonabelions通过一个超对称版本（拓扑通过A-扭曲）的这些规范西格玛模型的基态。这种分析是基于半经典近似的QFT通过超对称量子力学在其经典模空间。

英文摘要：

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 $Σ$, 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.

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