A requiem for AdS4× CP3 fermionic self-T duality

Strong evidence for dual superconformal symmetry in N=6 superconformal Chern-Simons theory has fueled expectations that the AdS/CFT dual geometry AdS4×CP3 is self-dual under T duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T duality, a symmetry originally proposed by Berkovits and Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T duality and comment on T duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T duality for AdS4×CP3 or its TsT deformations but leave the door open for new possibilities.