Fermionic T-duality in the pp-wave limit

AdS5 × S5 and its pp-wave limit are self-dual under transformations involving eight fermionic T-dualities, a property which accounts for symmetries seen in scattering amplitudes in N = 4 super-Yang-Mills. Despite strong evidence for similar symmetries in the amplitudes of three-dimensional N = 6 ABJM theory, a corresponding self-duality in the dual geometry AdS₄ × ℂP³ currently eludes us. Here, working with the type IIA ppwave limit of AdS₄ × ℂP³ preserving twenty four supercharges, we show that the pp-wave is self-dual with respect to eight commuting fermionic T-dualities and not the six expected. In addition, we show the same symmetry can be found in a superposition pp-wave and a generic pp-wave with twenty and sixteen unbroken supersymmetries respectively, strongly suggesting that self-duality under fermionic T-duality may be a symmetry of all pp-waves.