A note on unimodular N=1; d=4 AdS supergravity

We put forward a unimodular N = 1; d = 4 anti-de Sitter supergravity theory off shell. This theory, where the Cosmological Constant does not couple to gravity, has a unique maximally supersymmetric classical vacuum which is Anti-de Sitter spacetime with radius given by the equation of motion of the auxiliary scalar field, i.e., S = 3/kappa L. However, we see that the non-supersymmetric classical vacua of the unimodular theory are Minkowski and de Sitter spacetimes as well as anti-de Sitter spacetime with radius l not equal L