Supersymmetry: Boundary Conditions and Edge States
classification
✦ hep-th
cond-mat.mtrl-scicond-mat.supr-conmath-phmath.MP
keywords
boundaryconditionsmathcalsusystatesallowedboundariesbreak
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read the original abstract
When spatial boundaries are inserted, SUSY can be broken. We show that in an $\mathcal{N}=2$ supersymmetric theory, all the boundary conditions allowed by self-adjointness of the Hamiltonian break $\mathcal{N}=2$ SUSY while only a few of these boundary conditions preserve $\mathcal{N}=1$ SUSY. We also show that for a subset of the boundary conditions compatible with $\mathcal{N}=1$ SUSY, there exist fermionic ground states which are localized near the boundary.
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