AdS4 Radius & Cosmological Constant: Is n Relevant?

[gentsagree]

The AdS4 radius is related to the cosmological constant by $\Lambda =\frac{-3}{b^{2}}$.

Is this true in any number of dimensions, or is there a generalised relation depending on number of dimensions n?

 

[instanton]

In generic dimension $d$, the cosmological constant is related to AdS radius via $\Lambda=-\frac{(d-1)(d-2)}{2\ell^2}$.