In Supersymmetry and Morse Theory (1982) by E Witten,

Concern whether the supersymmetry is broken by checking whether
$$
Q | 0 \rangle=0
$$
exists or not --- Witten said:

SUSY breaking: A solution may be shown not to exist by calculating a reliable, positive lower bound to the energy eigenvalues.

SUSY non-breaking: It may be shown that a solution does exist by showing that the theory has a mass gap so that there is no potential "Goldstone fermion".

my question is that why SUSY non-breaking has something to do with

- no potential "Goldstone fermion"?
- theory has a mass gap?

Are these if and only if conditions?

$$
\text{Supersymmetry non-breaking} \iff \text{mass gap and no "Goldstone fermion"?}
$$

This post imported from StackExchange Physics at 2020-12-12 20:07 (UTC), posted by SE-user annie marie heart