Dual Gravitons in AdS 4 /CFT 3 and the Holographic Cotton Tensor (original) (raw)
We argue that gravity theories in AdS 4 are holographically dual to either of two threedimensional CFT's: the usual Dirichlet CFT 1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT 2 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 CFT 1 lead to a non-zero vev of the stress-energy tensor in CFT 2 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.
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