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Multiplets of superconformal symmetry in diverse dimensions

  • Clay CórdovaEmail author
  • Thomas T. Dumitrescu
  • Kenneth Intriligator
Open Access
Regular Article - Theoretical Physics
  • 27 Downloads

Abstract

We systematically analyze the operator content of unitary superconformal multiplets in d ≥ 3 spacetime dimensions. We present a simple, general, and efficient algorithm that generates all of these multiplets by correctly eliminating possible null states. The algorithm is conjectural, but passes a vast web of consistency checks. We apply it to tabulate a large variety of superconformal multiplets. In particular, we classify and construct all multiplets that contain conserved currents or free fields, which play an important role in superconformal field theories (SCFTs). Some currents that are allowed in conformal field theories cannot be embedded in superconformal multiplets, and hence they are absent in SCFTs. We use the structure of superconformal stress tensor multiplets to show that SCFTs with more than 16 Poincaré supercharges cannot arise in d ≥ 4, even when the corresponding superconformal algebras exist. We also show that such theories do arise in d = 3, but are necessarily free.

Keywords

Conformal and W Symmetry Conformal Field Theory Global Symmetries Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Clay Córdova
    • 1
    Email author
  • Thomas T. Dumitrescu
    • 2
  • Kenneth Intriligator
    • 3
  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  2. 2.Department of PhysicsHarvard UniversityCambridgeU.S.A.
  3. 3.Department of PhysicsUniversity of California, San DiegoLa JollaU.S.A.

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