| We discuss two aspects of AdS/CFT. The first is the compactification and consistent truncation of type IIB supergravity on a five-dimensional squashed Sasaki-Einstein manifold. The second is an extension of the holographic c-theorem in arbitrary even dimensions to the case of bulk actions built out of higher curvature terms.;We first derive the full bosonic and fermionic spectrum of fields for IIB super-gravity compactified on a five-dimensional squashed Sasaki-Einstein manifold. Under certain ansatz, we truncate the ten dimensional fields of IIB supergravity into five dimensional fields up to the second Kaluza-Klein tower. The consistency of the truncation is proved. We group the Kaluza-Klein modes up to the second level into super-conformal field theory multiplets, and discuss potential applications of such truncations for the AdS/condensed matter correspondence.;On the c-theorem side, we extend the holographic c-theorem proof into arbitrary even-dimensional gravity built of Lovelock terms. We also explore additional conditions that holographic c-theorems hold for the gravity action built of arbitrary f(R) and f( Rabcd) higher derivative terms. |
