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Monopole operators, moduli spaces and dualities

  • David Berenstein
  • Mauricio Romo
Article

Abstract

We develop a semiclassical method to analyze the spectrum of BPS monopole operators of three-dimensional superconformal field theories with \( \mathcal{N} \) = 2 supersymmetry. We show that the chiral ring of the theory results from the semiclassical holomorphic quantization of the solution of classical BPS equations of motion on the cylinder. We apply this formalism to various theories. We also use these techniques to compare the chiral rings of theories that might be related to each other via Seiberg dualities in four dimensions in the classical limit. We find that the change of basis transformations that generate dualities in four dimensions (homological operations) generically do not work in three dimensions in the presence of Chern-Simons terms. Instead, new theories generally arise this way. When dualities are possible, the Chern-Simons couplings need to satisfy certain arithmetic congruences. We also determine the spectrum of R-charges of the chiral ring operators by assembling them on a Hilbert series and by minimizing the coefficient of the maximum pole relative to the trial R-charge. This is related to volume minimization in theories with dual supergravity setups.

Keywords

Solitons Monopoles and Instantons AdS-CFT Correspondence ChernSimons Theories 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of California Santa Barbara (UCSB)Santa BarbaraU.S.A
  2. 2.School of Natural Sciences, Institute for Advanced StudyPrincetonU.S.A

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