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arXiv · 1609.03254

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

E. Ó Colgáin·A. Pittelli
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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.

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E. Ó Colgáin, A. Pittelli. 2016-09-12. A Requiem for $AdS_4 \times \mathbb{C} P^3$ Fermionic self-T-duality. https://doi.org/10.1103/physrevd.94.106006

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