Nonmetricity and torsion induced by dilaton gravity in two dimension

TL;DR

This paper explores a two-dimensional dilaton gravity model with nonmetricity and torsion, analyzing how spinor fields couple to the geometry and finding no nontrivial dilaton-spinor couplings.

Contribution

It develops a theory coupling Dirac spinors, dilaton, and non-Riemannian gravity, and examines the nature of these couplings in a reformulated Levi-Civita connection framework.

Findings

Exact solutions without spinors are presented.

Minimal spinor couplings do not produce nontrivial dilaton interactions.

The theory clarifies the role of nonmetricity and torsion in dilaton gravity.

Abstract

We develop a theory in which there are couplings amongst Dirac spinor, dilaton and non-Riemannian gravity and explore the nature of connection-induced dilaton couplings to gravity and Dirac spinor when the theory is reformulated in terms of the Levi-Civita connection. After presenting some exact solutions without spinors, we investigate the minimal spinor couplings to the model and in conclusion we can not find any nontrivial dilaton couplings to spinor.