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Mirror Symmetry p.200/201

Last section p.200/first p.201

It says, that the localization principle would not work if one would not impose periodic boundary conditions for the fermion integration, cause there would not be a supersymmetry to begin with.

Can anyone explain why this is so? I somehow do not get that argument.

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The engine behind path integral localization is SUSY. The issue is that in order for the infinitesimal SUSY transformation (10.165) on p. 199 to be well-defined, the right and left-hand sides of the eq. (10.165) must obey the same boundary condition (BC). Since the boson obeys periodic BC, the fermion must as well.

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