Algebraic structure of Gravity with Torsion

TL;DR

This paper explores the algebraic structure of gravity theories incorporating torsion, utilizing BRS transformations and Maurer-Cartan conditions to analyze invariants and anomalies in a systematic way.

Contribution

It introduces a novel approach to analyze gravity with torsion using Maurer-Cartan horizontality and a decomposition operator for BRS transformations.

Findings

Derived BRS transformations for gravity with torsion.

Solved Wess-Zumino consistency conditions for invariants and anomalies.

Provided a framework for algebraic analysis of torsional gravity theories.

Abstract

The BRS transformations for gravity with torsion are discussed by using the Maurer-Cartan horizontality conditions. With the help of an operator $\d$ which allows to decompose the exterior space-time derivative as a BRS commutator we solve the Wess-Zumino consistency condition corresponding to invariant Lagrangians and anomalies.