Fermionic T-duality in the pp-wave limit

Abstract

AdS 5 × S 5 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 $ \mathcal{N} = 4 $ super-Yang-Mills. Despite strong evidence for similar symmetries in the amplitudes of three-dimensional $ \mathcal{N} = 6 $ ABJM theory,a corresponding self-duality in the dual geometry $ Ad{S_4} \times \mathbb{C}{P^3} $ currently eludes us. Here, working with the type IIA pp-wave limit of $ Ad{S_4} \times \mathbb{C}{P^3} $ 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.