Fermions, differential forms and doubled geometry

Krasnov, Kirill

Abstract

© 2018 The Author We show that all fermions of one generation of the Pati–Salam version of the Standard Model (SM) can be elegantly described by a single fixed parity (say even) inhomogeneous real-valued differential form in seven dimensions. In this formalism the full kinetic term of the SM fermionic Lagrangian is reproduced as the appropriate dimensional reduction of (Ψ,DΨ) where Ψ is a general even degree differential form in R7, the inner product (⋅,⋅) is as described in the main text, and D is essentially an appropriately interpreted exterior derivative operator. The new formalism is based on geometric constructions originating in the subjects of generalised geometry and double field theory.

Citation

Krasnov, K. (2018). Fermions, differential forms and doubled geometry. Nuclear Physics B, 936, 36-75. https://doi.org/10.1016/j.nuclphysb.2018.09.006

• Journal Article Type: Article
• Acceptance Date: Sep 9, 2018
• Online Publication Date: Sep 13, 2018
• Publication Date: 2018-11
• Deposit Date: Sep 24, 2018
• Publicly Available Date: Sep 24, 2018
• Journal: Nuclear Physics B
• Print ISSN: 0550-3213
• Electronic ISSN: 1873-1562
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 936
• Pages: 36-75
• DOI: https://doi.org/10.1016/j.nuclphysb.2018.09.006
• Keywords: Nuclear and High Energy Physics
• Public URL: https://nottingham-repository.worktribe.com/output/1129028
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0550321318302530?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Fermions, differential forms and doubled geometry; Journal Title: Nuclear Physics B; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.nuclphysb.2018.09.006; Content Type: article; Copyright: © 2018 The Author. Published by Elsevier B.V.
• Contract Date: Sep 24, 2018