TY - JOUR
T1 - Hodge duality and supergravity
AU - Castellani, Leonardo
AU - Grassi, Pietro Antonio
N1 - Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
PY - 2023/8/15
Y1 - 2023/8/15
N2 - 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 the 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.
AB - 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 the 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.
UR - http://www.scopus.com/inward/record.url?scp=85172788939&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.108.046018
DO - 10.1103/PhysRevD.108.046018
M3 - Article
SN - 2470-0010
VL - 108
JO - Physical Review D
JF - Physical Review D
IS - 4
M1 - 046018
ER -