Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary

Abstract

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons theory which can either viewed as a boundary generating functional or as a boundary effective action.

25 pages; v2: minor improvements, references added

References in corpus (11)

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• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Setting the boundary free in AdS/CFT
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Cited by in corpus (3)

• Dual Gravitons in AdS4/CFT3 and the Holographic Cotton Tensor
• Torsion and the Gravity Dual of Parity Symmetry Breaking in AdS4/CFT3 Holography
• Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem