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

References in corpus (18)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gluon scattering amplitudes at strong coupling
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• The Bethe ansatz for superconformal Chern-Simons
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• On the fermionic T-duality of the AdS_4 \times CP^3 sigma-model
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• On AdS_4 x CP^3 T-duality
• Fermionic T-duality: A snapshot review
• Real fermionic symmetry in type II supergravity

Cited by in corpus (1)

• Dual conformal transformations of smooth holographic Wilson loops