Conformal Invariance in Einstein-Cartan-Weyl space

TL;DR

This paper explores conformally invariant actions across Einstein, Weyl, Einstein-Cartan, and Einstein-Cartan-Weyl geometries, revealing relations among them and expressing the actions using scalar fields, with implications for theoretical physics.

Contribution

It introduces a unified conformally invariant framework in various geometric spaces and expresses the actions with scalar fields, advancing understanding of their interrelations.

Findings

Derived conformally invariant actions in multiple geometries.

Linked observational conditions to equations of motion.

Expressed actions using scalar fields with specific conformal weights.

Abstract

We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb-Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.