Canonical Quantization of Scalar Fields — Mark Srednicki
Physics — QFT · oraifeartaigh-model-susy-breaking
Problem
Consider a supersymmetric theory with three chiral superfields A, B, and C, and a superpotential W=mBC+κA(C2−v2), where m and v are parameters with dimensions of mass, and κ is a dimensionless coupling constant. This is the O'Raifeartaigh model.
a) Show that one or more F components is nonzero at the minimum of the potential, and hence that supersymmetry is spontaneously broken.
b) Show that the potential is minimized along a line in field space, and find the masses of the particles at an arbitrary point on this line. You should find that there is a massless Goldstone fermion or goldstino that is related by supersymmetry to the linear combination of F fields that gets a nonzero vacuum expectation value.