Supersymmetry Properties of AdS Supergravity Backgrounds

Anti-de Sitter supergravity backgrounds are of particular interest in light of the AdS/CFT correspondence, which relates them to dual conformal field theories on the boundary of the anti-de Sitter space. We have investigated the forms of the supersymmetries these backgrounds preserve by solving the Killing spinor equations on the anti-de Sitter components of these spaces. We have found that a supersymmetric AdS$_n$ background necessarily preserves $2^{\lfloor{n\over2}\rfloor} k$ supersymmetries for $n \leq 4$ and $2^{\lfloor{n\over2}\rfloor+1} k$ supersymmetries for $4< n \leq 7$, $k \in \bb{N}_{>0}$. Additionally, we have found that the Killing spinors of each background are exactly the zeroes of a Dirac-like operator constructed from the Killing spinor equations.