Fermions, differential forms and doubled geometry

• Published in: Nuclear physics. B Vol. 936; pp. 36 - 75
• Main Author: Krasnov, Kirill
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2018; Elsevier
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/j.nuclphysb.2018.09.006

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.