Prepotentials for linearized supergravity
arXiv:1804.06729 · doi:10.1088/1361-6382/aafd40
Abstract
Linearized supergravity in arbitrary dimension is reformulated into a first order formalism which treats the graviton and its dual on the same footing at the level of the action. This generalizes previous work by other authors in two directions: 1) we work in arbitrary space-time dimension, and 2) the gravitino field and supersymmetry are also considered. This requires the construction of conformally invariant curvatures (the Cotton fields) for a family of mixed symmetry tensors and tensor-spinors, whose properties we prove (invariance; completeness; conformal Poincaré lemma). We use these geometric tools to solve the Hamiltonian constraints appearing in the first order formalism of the graviton and gravitino: the constraints are solved through the introduction of prepotentials enjoying (linearized) conformal invariance. These new variables (two tensor fields for the graviton, one tensor-spinor for the gravitino) are injected into the action and equations of motion, which take a geometrically simple form in terms of the Cotton tensor(-spinors) of the prepotentials. In particular, the equations of motion of the graviton are equivalent to twisted self-duality conditions. We express the supersymmetric transformations of the graviton and gravitino into each other in terms of the prepotentials. We also reproduce the dimensional reduction of supergravity within the prepotential formalism. Finally, our formulas in dimension five are recovered from the dimensional reduction of the already known prepotential formulation of the six-dimensional maximally supersymmetric theory.
arXiv commentv2: updated references
References in corpus (43)
- E_11 and M Theory
- Duality Symmetric Actions
- E10 and a "small tension expansion" of M Theory
- Dualisation of Dualities, I
- Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities
- Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma
- Duality, Self-Duality, Sources and Charge Quantization in Abelian N-Form Theories
- Duality in Gravity and Higher Spin Gauge Fields
- On geometric equations and duality for free higher spins
- Duality in linearized gravity
- Strongly Coupled Gravity and Duality
- Consistent deformations of dual formulations of linearized gravity: A no-go result
- Tensor fields of mixed Young symmetry type and N-complexes
- A note on spin-s duality
- No Self-Interaction for Two-Column Massless Fields
- Symmetries and Compactifications of (4,0) Conformal Gravity
- p-Brane Dyons and Electric-magnetic Duality
- Gravitational Duality Transformations on (A)dS4
- Duality invariance of all free bosonic and fermionic gauge fields
- Non-linear parent action and dual gravity
- Gravitational duality near de Sitter space
- S-Duality for Linearized Gravity
- E7(7) invariant Lagrangian of d=4 N=8 supergravity
- Free Spin 2 Duality Invariance Cannot be Extended to GR
- Dual Double Field Theory
- The Action for Twisted Self-Duality
- Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields
- Duality invariance implies Poincare invariance
- Off-Shell Hodge Dualities in Linearised Gravity and E11
- Manifest spin 2 duality with electric and magnetic sources
- Chiral Tensors of Mixed Young Symmetry
- Massless spin-two field S-duality
- Gravitational Electric-Magnetic Duality, Gauge Invariance and Twisted Self-Duality
- Twisted Self-Duality for Linearized Gravity in D dimensions
- Twisted self-duality for higher spin gauge fields and prepotentials
- Dual actions for massless, partially-massless and massive gravitons in (A)dS
- Supersymmetric electric-magnetic duality as a manifest symmetry of the action for super-Maxwell theory and linearized supergravity
- The Action of the (free) -theory
- Supersymmetric electric-magnetic duality of hypergravity
- Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields
- Frame-like off-shell dualisation for mixed-symmetry gauge fields
- A note on "gaugings" in four spacetime dimensions and electric-magnetic duality
- A deformation of the Curtright action