Fermions, differential forms and doubled geometry

TL;DR

This paper presents a novel geometric formalism using differential forms in seven dimensions to describe all fermions of one Standard Model generation, connecting to generalized geometry and double field theory.

Contribution

It introduces a unified differential form framework for fermions in the Standard Model, leveraging concepts from generalized geometry and double field theory.

Findings

Reproduces the SM fermionic kinetic term via dimensional reduction.

Provides a geometric interpretation of fermions using differential forms.

Connects fermionic descriptions to advanced geometric theories.

Abstract

We show that all fermions of one generation 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 (Psi, D Psi) where Psi is a general even degree differential form in R^7, 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.