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Strong evidence for dual superconformal symmetry in $\mathcal{N} = 6$superconformal Chern-Simons theory has fueled expectations that the AdS/CFTdual geometry $AdS_4 \times \mathbb{C} P^3$ is self-dual under T-duality. Werevisit the problem to identify commuting bosonic and fermionic isometries in asystematic fashion and show that fermionic T-duality, a symmetry originallyproposed by Berkovits & Maldacena, inevitably leads to a singularity in thedilaton transformation. We show that TsT deformations commute with fermionicT-duality and comment on T-duality in the corresponding sigma model. Ourresults rule out self-duality based on fermionic T-duality for $AdS_4 \times\mathbb{C} P^3$ or its TsT deformations, but leave the door open for newpossibilities.

A Requiem for $AdS_4 \times \mathbb{C} P^3$ Fermionic self-T-duality