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In theories with extended supersymmetry, both short and long multiplets exist. For some reason or other, short multiplets are studied more often. Why? What's wrong with long multiplets?

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Though I don't understand the full argument myself, much of the interest interest about short and long multiplets comes from wanting to calculate the superconformal index. The way these indices are defined they count short multiplets modulo those which can add up to long multiplets. I guess the idea is that the regime of the deformation parameters of the theory where short multiplets start adding up into long ones is not reachable by continuous variation of the parameters and there the index loses its meaning. I would be glad to know of an expository reference which explains this point. –  user6818 Apr 11 '11 at 15:00

1 Answer 1

Long multiplets are bad because they have an unnecessarily high mass. This fact usually makes them

  • unstable because lighter objects with the same conserved charges exist
  • decouple from low-energy physics which often comes from short multiplets
  • contribute zero to the indices that can be calculated in various ways (they always contribute zero!)
  • impossible to be exactly calculated with - because their mass or energy is unconstrained by symmetries and, in this sense, arbitrary

Short multiplets have the corresponding virtues. Invert the four points above.

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"Invert the four points above." -> tsixe segrahc devresnoc emas eht htiw stcejbo rethgil esuaceb elbatsnu stelpitlum trohs morf semoc netfo hcihw scisyhp ygrene-wol morf elpuoced )!orez etubirtnoc syawla yeht( syaw suoirav ni detaluclac eb nac taht secidni eht ot orez etubirtnoc yrartibra ,esnes siht ni ,dna seirtemmys yb deniartsnocnu si ygrene ro ssam rieht esuaceb - htiw detaluclac yltcaxe eb ot elbissopmi -- makes sense. +1 for the answer though :) –  Marek Apr 11 '11 at 18:23
@Marek 8-| Tell me you didn't go through the trouble of typing that out. –  dbrane Apr 11 '11 at 22:19
@dbrane: I wished I could tell you that I did but unfortunately I cheated and used the $\tt rev$ command. –  Marek Apr 11 '11 at 23:50

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