  AdS5 X 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 X CP3 currently eludes us.
Here, working with the type IIA pp-wave limit of AdS4 X 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.
