Supergravity on $AdS_{5/4} \times$ Hopf Fibrations and Conformal Field Theories

Abstract

We obtain three and four dimensional conformal field theories with less than maximal supersymmetry by using their supergravity duals. These supergravity theories are type II on $AdS_5 \times CP^2$, IIA on $AdS_4 \times CP^3$, IIB on $AdS_5 \times S^5/Z_k$ and D=11 supergravity on $AdS_4 \times S^7/Z_k$. They are obtained from the spherically compactified ten and eleven dimensional theories by either Hopf reduction or by winding the U(1) fiber over the base.