Supersymmetry in Anti‐de Sitter Space

We review the renormalization of the ground state solution of extended supergravity and super‐symmetric Kaluza‐Klein theories. The computation of an adiabatic expansion of the effective action to the one‐loop order yields the result that a linear superfield insertion in the superpotential is needed, in order to renormalize the nonvanishing one‐particle‐irreducible one‐point functions, whereas supersymmetry is preserved at each extremum of the effective potential. The calculation of the one‐particle‐irreducible two‐and three‐point functions shows that neither the mass nor the interaction lagrangians get renormalized to the one‐loop order. We conclude that the one‐loop effects proportional to the contraction parameter of the curved background space force a violation of the no‐renormalization theorem.