Non-extended and extended SUSY

Question

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

Comments

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

Answer 1

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.

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