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arXiv · 1503.00526

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

Indranil Biswas·Nuno M. Romão
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Abstract

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.

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Indranil Biswas, Nuno M. Romão. 2015-03-02. A no-go theorem for nonabelionic statistics in gauged linear sigma-models. https://arxiv.org/abs/1503.00526

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