On the Algebraic Structure of Gravity with Torsion including Weyl symmetry

TL;DR

This paper explores the algebraic structure of gravity theories with torsion and Weyl symmetry using BRST transformations, Maurer-Cartan conditions, and analyzes scalar matter coupling, anomalies, and invariant Lagrangians.

Contribution

It introduces a BRST framework for gravity with torsion and Weyl symmetry, solving consistency conditions and incorporating matter fields.

Findings

Derived BRST transformations for gravity with torsion and Weyl symmetry

Solved Wess-Zumino consistency conditions for invariant Lagrangians and anomalies

Extended analysis to include scalar matter coupling

Abstract

The BRST transformations for gravity with torsion including Weyl symmetry are discussed by using the so-called Maurer-Cartan horizontality conditions. Also the coupling of scalar matter fields to gravity is incorporated in this analysis. With the help of an operator $\d$ which allows to decompose the exterior space-time derivative as a BRST commutator we solve the Wess-Zumino consistency condition corresponding to invariant Lagrangians and anomalies for the cases with and without Weyl symmetry.