1) That's not the only ingredient -- it's a prerequisite for holography. In reality, with holographic duality one always means a precise mapping from observables in a gravity theory in AdS to observables in a CFT that lives on the boundary. So holography is much richer: it prescribes for example how you can compute a Wilson loop on the boundary CFT in terms of gravity.

2) No, it's in fact almost trivial. $AdS_{d+1}$ with radius $R$ can be defined as the solution to

$$ \eta_{\mu \nu} X^\mu X^\nu = R^2 $$

with $\eta_{\mu \nu} = (1,1,-1,\ldots,-1)$ and where $X^\mu$ lives in $\mathbb{R}^{d+2}$. But $SO(2,d)$ is precisely the group that leaves the quadratic form $\eta_{\mu \nu} X^\mu X^\nu$ invariant.

If this is too abstract, think of the sphere $S^2$. It can be defined as the set of points $X^\mu \in \mathbb{R}^3$ that obey

$$ \delta_{\mu \nu} X^\mu X^\nu = R^2.$$

Its isometry group is $SO(3)$ because this leaves $X^2$ invariant.

This post imported from StackExchange Physics at 2016-01-06 09:18 (UTC), posted by SE-user Hans Moleman