On Dual Formulation of Gravity

Abstract

In this paper we consider a possibility to construct dual formulation of gravity where the main dynamical field is the Lorentz connection ω_μ^{ab} and not that of tetrad e_μ^a or metric g_μν. Our approach is based on the usual dualization procedure which uses first order parent Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It turns out that in d=3 dimensions such dual formulation is related with the so called exotic parity-violating interactions for massless spin-2 particles.

7 pages, plain LaTeX

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• Off-Shell Hodge Dualities in Linearised Gravity and E11
• Dual actions for massless, partially-massless and massive gravitons in (A)dS
• On Dual Formulation of Gravity
• A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS
• Dual Linearised Gravity in Arbitrary Dimensions
• Frame-like off-shell dualisation for mixed-symmetry gauge fields
• Spin-2 twisted duality in (A)dS
• Pure Lorentz spin connection theories and uniqueness of General Relativity
• On Dual Formulation of Gravity. II. Metric and Affine Connection