N=1 SUSY: How Many Superpartners for a Boson/Fermion?

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SUMMARY

In N=1 Supersymmetry (SUSY), each boson has a corresponding fermionic partner, along with an auxiliary field. For N>1, the number of superpartners for a boson or fermion is determined by the number of fermions in a multiplet, which is equal to N. For instance, in N=2 SUSY, there are 2 Weyl fermions, resulting in 4 on-shell fermionic degrees of freedom. This configuration allows for either 2 complex scalar fields (a "Hypermultiplet") or a combination of 1 complex scalar field and 1 massless gauge field (a "Vector Multiplet") to maintain supersymmetry.

PREREQUISITES
  • N=1 and N=2 Supersymmetry concepts
  • Understanding of bosons and fermions
  • Fermionic multiplets in SUSY
  • Basic knowledge of complex scalar fields and gauge fields
NEXT STEPS
  • Study the implications of N=2 SUSY on particle physics
  • Explore the properties of Weyl fermions in supersymmetric theories
  • Investigate the construction of Hypermultiplets and Vector Multiplets
  • Learn about the role of auxiliary fields in SUSY models
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Particle physicists, theoretical physicists, and students interested in advanced concepts of supersymmetry and its implications in particle interactions.

Femto
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I am sorry if the question is naive. In N=1 SUSY, for every boson we have a fermionic partner (and an auxilliary field) and vice-versa. When N>1 how many superpartners do we have given a boson (or a fermion)? Is it N?
 
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N is the number of fermions in a given multiplet (for linearly realized SUSY, but that's a technicality).

Ex: for N=2, there are 2 (Weyl) fermions and therefore 4 (onshell) fermionic degrees of freedom. therefore you can either have 2 complex scalar fields (called a "Hypermultiplet"), or 1 complex scalar field and one massless gauge field (called a "Vector Multiplet") to make it supersymmetric.

etc.
 

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