Gravitational Electric-Magnetic Duality, Gauge Invariance and Twisted Self-Duality

Abstract

The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is manifestly invariant under duality rotations in the internal 2-plane of the spacetime curvature and its dual. In order to achieve this manifestly duality-invariant form, it is necessary to introduce two "prepotentials", which form a duality multiplet. These prepotentials enjoy interesting gauge invariance symmetries, which are, for each, linearized diffeomorphisms and linearized Weyl rescalings. The purpose of this note is twofold: (i) To rewrite the manifestly-duality invariant action obtained in previous work in a way that makes its gauge invariances also manifest. (ii) To explicitly show that the equations of motion derived from that action can be interpreted as twisted self-duality conditions on the curvature tensors of the two metrics obtained from the two prepotentials.

Invited contribution to the J Phys A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Misha Vasiliev. Misprints corrected, two footnotes added

References in corpus (5)

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Cited by in corpus (20)

• Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields
• Manifest Duality for Partially Massless Higher Spins
• Chiral Tensors of Mixed Young Symmetry
• Twisted Self-Duality for Linearized Gravity in D dimensions
• Covariant fracton gauge theory with boundary
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Twisted self-duality for higher spin gauge fields and prepotentials
• Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity
• The Action of the (free) $(4,0)$-theory
• Supersymmetric electric-magnetic duality of hypergravity
• Integrability, Einstein spaces and holographic fluids
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
• Prepotentials for linearized supergravity
• Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS
• Gravitational Fields of the Magnetic-type
• Manifest electric-magnetic duality in linearized conformal gravity
• Aspects of electric-magnetic dualities in maximal supergravity
• Electromagnetic duality and central charge from first order formulation
• New Reflections on Gravitational Duality
• Gravielectric and gravimagnetic fluxes in nutty black holes