Supersymmetry breaking and vacuum energy on anti-de sitter space

This paper examines the connection between the vacuum energy and the spontaneous breaking of supersymmetry in anti-de Sitter space. It is shown that in any supersymmetric theory, when quantized on a classical anti-de Sitter background admitting Killing spinors, the supersymmetry is never broken by one-loop effects. The vacuum expectation value of the “bare” stress tensor is argued to be zero if and only if supersymmetry is unbroken. Consequently the bare vacuum stress energy always vanishes for such a theory. It is then shown that the renormalized stress-energy need not vanish and a simple prescription for its one-loop calculation is given. Since it is the renormalized energy which determines the quantum corrections to the curvature of the background anti-de Sitter space these corrections are also easily found. It is shown that these corrections vanish for any one-loop finite theory. For SO(N) gauged extended supergravity these corrections need not be zero but always tend to decrease the curvature of the AdS space.