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Monopole Operators and Mirror Symmetry in Three-Dimensional Gauge Theories


Borokhov, Vadim Aleksandrovich (2004) Monopole Operators and Mirror Symmetry in Three-Dimensional Gauge Theories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5AP4-X614.


Many 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 that are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogs of twist and winding-state operators in free 2-D 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 gauge theories using large N_f expansion. For non-supersymmetric gauge theories we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We demonstrate that these monopole operators transform non-trivially under the flavor symmetry group.

We also consider topology-changing operators in the infrared limits of N=2 and N=4 supersymmetric QED as well as N=4 SU(2) gauge theory in three dimensions. Using large N_f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators that are primaries of short representation of the superconformal algebra and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified. Furthermore, we argue that some of our large-N_f results are exact. This implies, in particular, that certain monopole operators in N=4 3-D SQED with N_f=1 are free fields. This amounts to a proof of 3-D mirror symmetry in these special cases.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:duality; large N expansion; monopole; supersymmetry; three-dimensional gauge theories
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Group:Caltech Theory
Thesis Committee:
  • Kapustin, Anton N. (chair)
  • Porter, Frank C.
  • Schwarz, John H.
  • Wise, Mark B.
Defense Date:31 March 2004
Record Number:CaltechETD:etd-04062004-015855
Persistent URL:
Borokhov, Vadim Aleksandrovich0000-0001-6230-0672
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1275
Deposited By: Imported from ETD-db
Deposited On:08 Apr 2004
Last Modified:06 Jan 2021 00:26

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