OSp(N,4)-invariant dimensional regularization

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Abstract
We determine the effect of the background geometry exactly in the calculation of the one-loop effective potential of the Wess-Zumino model in anti–de Sitter space. The calculation of the semiclassical vacuum solutions is performed using Green’s functions which propagate fields in n-dimensional anti–de Sitter space. We show how to deal with the reflective boundary conditions at spatial infinity imposed by classical supersymmetry invariance on the field propagators. We address the question of the survival of the classical supersymmetry invariance of the vacuum state, when quantum corrections are taken into account. Our result is the persistence of supersymmetry to the one-loop order.