Dual Gravitons in AdS4/CFT3 and the Holographic Cotton Tensor

Abstract

We argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the renormalized stress-energy tensor is the electric field and the Cotton tensor is the magnetic field. Generic Robin boundary conditions lead to CFT's coupled to Cotton gravity or topologically massive gravity. Interaction terms with CFT1 lead to a non-zero vev of the stress-energy tensor in CFT2 coupled to gravity even after the source is removed. We point out that the dual graviton also exists beyond the linearized approximation, and spell out some of the details of the non-linear construction.

31 pages

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• $\mathcal{N}=2$ AdS${}_4$ supergravity, holography and Ward identities
• Torsional degrees of freedom in AdS4/CFT3
• Aspects of topologically gauged M2-branes with six supersymmetries: towards a "sequential AdS/CFT"?
• Radiation in Fluid/Gravity and the Flat Limit
• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• Gravitational duality, topologically massive gravity and holographic fluids
• Instantons and the Hartle-Hawking-Maldacena Proposal for dS/CFT
• The Invisibility of Diffeomorphisms
• Dual photons and gravitons
• Nonperfect Carrollian Fluids Through Holography