A Study of Fermions Coupled to Gauge and Gravitational Fields on a Cylinder

TL;DR

This paper investigates fermions on a cylindrical geometry coupled to gravity and gauge fields, revealing constraints on gauge coupling, effects of gravity on masses, and proposing a new gravitational theory linked to fermions.

Contribution

It introduces a novel gravitational theory coupling to fermions by making the coadjoint vector of diffeomorphisms dynamical, and shows the system reduces to a one-dimensional model.

Findings

Gauge coupling constant is constrained by the system's symmetries.

Gravity influences the fermion masses in the model.

The proposed gravitational theory simplifies to a one-dimensional system.

Abstract

Fermions on a cylinder coupled to gravity and gauge fields are examined by studying the geometric action associated with the symmetries of such a system. The gauge coupling constant is shown to be constrained and the effect of gravity on the masses is discussed. Furthermore, we introduce a new gravitational theory which couples to the fermions by promoting the coadjoint vector of the diffeomorphism sector to a dynamical variable. This system, together with the gauge sector is shown to be equivalent to a one dimensional system.