# Dynamical supersymmetry breaking and Witten index

Witten index, defined as ${\rm Tr}(-1)^F$, makes know if supersymmetry is spontaneously broken or not for a given model. But it is known that supersymmetry can be also broken dynamically and one can think of a mechanism (yet to be implemented if any) a la Nambu-Jona-Lasinio model for chiral symmetry in QCD. In this case, how does Witten index change? I think it should reflect the fact that, even if we are not requiring explicitly a selected ground state breaking symmetry, particle masses are lifted and a gap equation is satisfied.

A more general question is if Witten index applies as well to dynamical breaking of supersymmetry, for all the models one can possibly conceive.

As usual, good references are welcome.

Thanks.

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When ${\rm Tr}(-1)^F\neq 0$, then supersymmetry cannot be spontaneously broken. One could say that this basic fact is the very point of the Witten index.

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Yes, I know this. I have read Witten's paper. But how does this idea translate to dynamical breaking of symmetry? And if I would have a NJL mechanism? –  Jon Nov 29 '12 at 9:58