# On Goldstone fermions / goldstino: SUSY breaking

+ 0 like - 0 dislike
359 views

There are statements about Goldstone fermions, or goldstino, seem confusing to me.

(1) Goldstone boson requires a continuous symmetry spontaneously broken. Does Goldstone fermion imply continuous SUSY spontaneously broken? But boson B and fermion F Hilbert space can be finite dimensional and discrete. The number of SUSY charge $$\mathcal{N}$$ is also discrete. What do we mean by continuous SUSY if there is ? If not, how does the Goldstone theorem on the continuous global symmetry applies to SUSY (possibly discrete, switching between bosonic B and fermionic F sector, and finite $$\mathcal{N}$$)?

(2) In Witten 1982 NPB - Constraints on Supersymmetry Breaking, he said:

(A) the number of boson zero energy modes $$n_b=0$$ and fermion zero energy modes $$n_f=0$$ --- supersymmetry is spontaneously broken and there is a massless Goldstone fermion in the infinite volume theory.

• How and why the massless Goldstone fermion appears, only in the infinite volume limit? (only when the states of bosonic B and fermionic F sector become infinite?) How to interpret Goldstone fermion when we have a finite size but large $$L$$ system?

(B) the number of boson vs fermion zero energy modes $$n_b= n_f\neq 0$$, supersymmetry is not broken; there is no Goldstone fermion, but there are zero-energy fermionic states which we interpret as evidence that the infinite volume theory has a massless fermion (a massless fermion is not a Goldstone fermion unless it is created from the vacuum by the supersymmetry current).

• How do we know there is a massless fermion (in the infinite volume)?

• How to show Goldstone fermion is created from the vacuum by the supersymmetry current? (in the infinite volume? How to interpret it in the finite volume?)

This post imported from StackExchange Physics at 2020-12-13 12:43 (UTC), posted by SE-user annie marie heart
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOve$\varnothing$flowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). Please complete the anti-spam verification