Non-extended and extended SUSY

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1. What are the distinctions between Non-extended SUSY and Extended SUSY?

(Is that just a non-extended SUSY has $$\mathcal{N}=1$$ while the extended SUSY has $$\mathcal{N}>1$$ ? Then there is no conceptual upgrade?)

2.

• If we start from a non-extended SUSY, how to obtain an extended SUSY?

• If we start from an extended SUSY , how to obtain a non-extended SUSY?

(via SUSY breaking? what else?)

This post imported from StackExchange Physics at 2020-12-12 20:06 (UTC), posted by SE-user annie marie heart
retagged Dec 12, 2020
For 1, yes it is just a matter of $\mathcal{N}$ I believe. Regarding 2, it is probably not what you are interested in, but note that you can construct (maximally) extended $\mathcal{N}=4$ SUSY in $4$d by dimensional reduction from $\mathcal{N}=1$ SUSY in $10$d.

This post imported from StackExchange Physics at 2020-12-12 20:06 (UTC), posted by SE-user Jxx

1. One can get extended SUSY by combining two supersymmetric multiplets into one with the appropriate choice of coupling constant. For example - in order to get $$\mathcal{N} = 2$$ SYM (Super Yang-Mills) one combines the gauge multiplet with gluon $$A_\mu$$ and gluino $$\lambda_\alpha$$ with the chiral multiplet with a fermion $$\psi_\alpha$$ and a scalar $$\phi$$, all fields in the adjoint representation of the gauge group. $$\begin{gather*} A_\mu \\ \lambda \qquad \psi \\ \phi \end{gather*}$$
2. Yes, one can "downgrade" the SUSY by symmetry breaking - for example in the famous artice by E.Witten and N.Seiberg "Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory" https://arxiv.org/abs/hep-th/9407087 - SUSY is broken from $$\mathcal{N} = 2$$ to $$\mathcal{N} = 1$$ by the superpotential term : $$W = m \text{Tr} \ \Phi^2$$ And this breaking is crucial for the monopole condensation and the description of confinement. I am not aware, unfortunately, of the other mechanisms of getting a symmetry with less SUSY in other way than the symmetry breaking by introducing soft or hard SUSY breaking terms or spontaneous SUSY breaking.
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