Beginner: Strings and space-time supersymmetry

Al.Rivero@gmail.com

I was wondering, OK it is a gedakenexperiment because it is beyond
observation, but... how is space-time supersymmetry (no worldsheet
susy) supossed to appear from the point of view of states of the
fundamental string? Do we observe entities with spin 0 and spin 1/2
having the same mass? And what happens for highly excited levels of the
string? If they mimic the QCD string, these excited levels have higher
spin. Do we have multiplets for, say, Spin 10 and spin 10 +- 1/2 ? Do
all these particles follow regge trajectories?

[Moderator's note: Yes, Alejandro, spacetime supersymmetry also has an
action on the worldsheet. Its existence is manifest in the Green-Schwarz
formalism - see chapter 5 of Green-Schwarz-Witten - while its existence
depends on seemingly miraculous identities such as Jacobi's obscure
formula - see chapter 4 of Green-Schwarz Witten. You can also see the
beginning of 2nd volume of Joe Polchinski's textbook, or many other
sources. Yes, spinning modes of the string with an arbitrarily high
spin have their superpartners whose spin differs by +-1/2 - or up to
+-2 in the case of maximal supersymmetry. Such superpartners lie
on the same Regge trajectory moved by +-1/2 or +-2 in the J direction.
Only one of these trajectories is really "leading" - one with maximal
J. Best wishes, LM]