A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality

Abstract

Strong evidence for dual superconformal symmetry in $\mathcal{N}=6$ superconformal Chern-Simons theory has fueled expectations that the AdS/CFT dual geometry $Ad{S}_4\times \mathbb{C}{P}^3$ 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 $Ad{S}_4\times \mathbb{C}{P}^3$ or its TsT deformations, but leave the door open for new possibilities.

v1 13 pages, 2 column; v2 13pages 2 column, title changed to better reflect content, two expressions deemed challenging to non-native English speakers reworded (outcome of peer review), to appear in PRD; v3 typo in metric in equation (33) corrected

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Cited by in corpus (13)

• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Super Non-Abelian T-Duality
• Non-abelian fermionic T-duality in supergravity
• Quantum noncommutative ABJM theory: first steps
• Non-commutative massive unquenched ABJM
• Dual conformal transformations of smooth holographic Wilson loops
• Fermionic T-duality of DFT
• ABJM flux-tube and scattering amplitudes
• Yangian Symmetry in Five Dimensions
• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory