Hodge Duality and Supergravity

2023/05/10 by Leonardo Castellani, Castellani, Leonardo, Pietro Antonio Grassi +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2305.06034

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The Hodge dual operator, recently introduced for supermanifolds, is used to reformulate super Yang-Mills and supergravity in D=4. We first recall the definition of the Hodge dual operator for flat and curved supermanifolds. Then we show how to recover the usual super-Yang-Mills equations of motion for N=1,2 supersymmetry, and the obstacles (as seen from Hodge dual point of view) in the case N ≥ 3. We reconsider several ingredients of supergeometry, relevant for a superspace formulation of supergravity, in terms of the Hodge dual operator. Finally we discuss how D=4 and N=1 supergravity is obtained in this framework.

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