Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice Z_N-Higgs Models

Details Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice Z_N-Higgs Models Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice Z_N-Higgs Models

1996-11-29

arxiv.org/abs/hep-th/9612007v1

Commun.Math.Phys. 191 (1998) 409-466

Physics

High Energy Physics

High Energy Physics - Theory

61 pages. LaTeX. AmsTeX fonts used.

Scientific paper

10.1007/s002200050273

We construct dyonic states in 2+1-dimensional lattice Z_N-Higgs models, i.e., states which are both, electrically and magnetically charged. The associated Hilbert spaces carry charged representations of the observable algebra, the global transfer matrix and a unitary implementation of the group of spatial lattice translations. We prove that for coinciding total charges these representations are dynamically equivalent and we construct a local intertwiner connection depending on a path in the space of charge distributions. The holonomy of this connection is given by Z_N-valued phases. This will be the starting point for a construction of scattering states with anyon statistics in a subsequent paper.

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