2018/04/30 by Victor Lekeu, Amaury Leonard
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Equations of motion #Gravitation #Gravitino #Graviton #Killing spinor #Mathematical physics #Noncommutative and Quantum Gravity Theories #Particle physics #Physics #Quantum mechanics #Spinor #Supergravity #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1088/1361-6382/aafd40
v2: updated references
openalex publication_date 2019/01/10 · arxiv created 2019/08/13 · arxiv updated 2019/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 of the graviton and gravitino through the introduction of prepotentials (two tensor fields for the graviton, one tensor-spinor for the gravitino) enjoying (linearized) conformal invariance. The action and equations of motion 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 6D maximally supersymmetric theory.