Vacua of M theory and string theory - art. no. 125003

We argue that supersymmetric higher-dimension operators in the effective ac tions of M theory and type IIB suing theory do not affect the maximally sup ersymmetric vacua: AdS(4)XS(7) and AdS(7)XS(4) in M theory and AdS(5)xS(5) in type IIB string theory. All these vacua are described in superspace by a fixed point with all components of supertorsion and supercurvature being s upercovariantly constant. This follows from 32 unbroken supersymmetries and allows us to prove that such vacua are exact. [S0556-2821(98)10520-9].