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Dual gravitons in $$AdS_{4}/CFT_{3}$$ and the holographic cotton tensor. (English) Zbl 1243.83068
Summary: We argue that gravity theories in $$AdS_{4}$$ are holographically dual to either of two three-dimensional 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.

##### MSC:
 83E30 String and superstring theories in gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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