On the Emergent Dynamics of Fermions in Curved Spacetime

TL;DR

This paper introduces a novel non-dynamical fermion theory in 3+1 dimensions, called spinor topological field theory, which recovers Dirac theory in curved spacetime and offers a geometric perspective on fermion mass.

Contribution

The work proposes a new spinor topological field theory based on Cartan connections related to the de Sitter group, providing a geometric origin for fermion mass and extending to include gauge fields and interactions.

Findings

Model reproduces Dirac theory in curved spacetime when gauge invariance breaks down.

Provides a geometric interpretation of fermion mass.

Framework allows inclusion of gauge fields and four-fermion interactions.

Abstract

Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor topological field theory, built in terms of a spinor field and a Cartan connection related to de Sitter group. We show that our model gives rise to the Dirac theory in curved spacetime when the local de Sitter gauge invariance of the model breaks down to the Lorentz gauge invariance, providing also a geometric origin to the fermion mass. Finally, we show that other gauge fields and suitable four-fermion interactions can be included in a straightforward way.