A modified gravity model coupled to a Dirac field in 2D spacetimes with quadratic nonmetricity and curvature

TL;DR

This paper develops a modified gravity model in 2D spacetimes with quadratic nonmetricity and curvature, coupling it to a Dirac field, deriving field equations, and exploring specific solutions including vacuum and Dirac backgrounds.

Contribution

It introduces a novel 2D gravity model with quadratic nonmetricity and curvature coupled to a Dirac field, deriving field equations and finding explicit solutions.

Findings

Derived field equations for the model.

Found classes of vacuum solutions.

Obtained a specific Dirac equation solution in a background.

Abstract

After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form which is quadratic in the nonmetricity and both linear and quadratic in the curvature in two dimensions. Subsequently we obtain field equations by varying the total Lagrangian with respect to the independent variables. Finally we find some classes of solutions of the vacuum theory and then a solution of the Dirac equation in a specific background and analyse them.