Supersymmetric Completion of an R2 Term in Five-Dimensional Supergravity

We analyze the structure of a particular higher derivative correction of five-dimensional ungauged and gauged supergravity with eight supercharges. Specifically, we determine all the purely bosonic terms which are connected by the supersymmetry transformation to the mixed gauge-gravitational Chern-Simons term, W tr R R. Our construction utilizes the superconformal formulation of supergravity. As an application, we determine the condition for the supersymmetric anti-de Sitter vacuum with this term. We check that it gives precisely the same condition as the a-maximization in four-dimensional superconformal field theory on the boundary, as predicted by the AdS/CFT correspondence. * ) Minimal supersymmetry in five dimensions has eight supercharges. This form of supersymmetry is usually called N = 2 in the supergravity literature and N = 1 in the field theory literature. We call it N = 2, following the supergravity convention. * ) As discussed in Ref. 6), the second and third constraints in (2 . 3) are avoidable and we can keep the gauge fields f a and i independent. Here, we impose the constraints to obtain simpler transformation laws. * ) We usually take the D gauge field b to be zero through K gauge fixing.