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

TL;DR

This paper investigates the potential for fermionic T-duality to establish self-duality of the $AdS_4 imes b{C}P^3$ background, finding that it inevitably leads to singularities and thus rules out such self-duality.

Contribution

The study systematically analyzes fermionic T-duality in $AdS_4 imes b{C}P^3$, demonstrating its incompatibility due to singularities, and explores the interplay with TsT deformations.

Findings

Fermionic T-duality causes singularities in the dilaton transformation.

TsT deformations commute with fermionic T-duality.

Self-duality via fermionic T-duality is ruled out for $AdS_4 imes b{C}P^3$.

Abstract

Strong evidence for dual superconformal symmetry in $\mathcal{N} = 6$ superconformal Chern-Simons theory has fueled expectations that the AdS/CFT dual geometry $AdS_4 \times \mathbb{C} P^3$ 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 & 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 $AdS_4 \times \mathbb{C} P^3$ or its TsT deformations, but leave the door open for new possibilities.