I would be glad if someone can explain to me the argument as to why supersymmetry breaking is necessarily accompanied by appearance of a massless fermion, namely the goldstino. (and also why this is a non-perturbative effect)
Let me quote here the two lines from the third volume of the QFT books by Weinberg where he tries to explain this phenomenon,
"(when supersymmetry is broken)..any n-particle state is accompanied with 2 states of the same energy and momentum and opposite statistics, containing an additional 0-momentum goldstino of spin up or down and with another state of the same energy and momentum and the same statistics, containing two additional 0-momentum goldstinos of opposite spin."
"In particular when supersymmetry is spontaneously broken the vacuum state has non-zero energy, so it must be paired with a fermionic state of the same energy and zero-momentum; more precisely, the vacuum and the state containing two zero-momentum goldstinos are paired with the two states of a single zero-momentum goldstino."
I am unable to understand the above two arguments and will be glad if someone can help.