Nuclear Physics B206 (1982) 413-439 © North-Holland Publishing Company INSTANTONS AND (SUPER-) SYMMETRY BREAKING IN (2+1) DIMENSIONS*

Unbroken supersymmetry requires degeneracy between Bose and Fermi degrees of f reedom [1]. Since no such degeneracy is actually observed, any supersymmetr ic model of nature must include a mechanism for supersymmetry breaking [2]. The scale of this breaking may be of order the Planck m a s s in which case only local supersymmetry (supergravity) is of relevance to the real world. If this is the case, then supersymmetry is relevant to particle physics at ordinary energies only in a very indirect fashion. In particular, it seems unclear how supersymmetry broken at the Planck mass could provide an explanation for why the mass scales of ordinary physics are so much smaller than the Planck mass. On the other hand, if supersymmetry is broken at energies of say a few TeV, it is quite plausible that this breaking could trigger the usual SU(2)L breaking if Higgs fields, which were forced to be massless by supersymmetry, acquired vacuum expectation values once supersymmetry was broken. However , one must still explain why the scale of supersymmetry breaking is so much less than the Planck mass. One attractive possibility would be that supersymmetry is unbroken in per turbation theory, but is "dynamically b roken" through small non-perturbat ive effects [3]. For this to happen, in a weakly coupled theory, a fermion must exist which is massless to all orders in per turbat ion theory but has no coupling to the supersymmerry current at zero momentum. If instantons induce such a coupling, this fermion becomes the Goldstino of spontaneously broken supersymmetry. Writing the zeromomen tum coupling as