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Published November 2002 | Published
Journal Article Open

Topological disorder operators in three-dimensional conformal field theory

Abstract

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N-f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N-f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.

Additional Information

© Institute of Physics and IOP Publishing Limited 2002. Received 6 November 2002, accepted for publication 26 November 2002. Published 7 January 2003. This work grew out of attempts by one of the authors (A.K.) and M. J. Strassler to improve on the last section of ref. [11]. A.K. would like to thank M. J. Strassler for numerous discussions which helped to realize the importance of fermionic zero modes. We also would like to thank J. Maldacena, T. Okuda, and H. Ooguri for useful conversations, and S. Sachdev for informing us about ref. [28]. This work was supported in part by a DOE grant DE-FG03-92-ER40701.

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