Topological 2-form Gravity in Four Dimensions

TL;DR

This paper proposes a topological field theory model for 2-form Einstein gravity in four dimensions, demonstrating its potential to provide exact quantum solutions and applying BRST quantization to analyze its structure.

Contribution

It introduces a novel topological field theory framework for 2-form Einstein gravity and performs BRST quantization, offering insights into quantum solutions of the theory.

Findings

A candidate theory yields exact solutions to the Wheeler-DeWitt equation.

BRST quantization is successfully applied to the topological 2-form gravity.

The approach provides a new perspective on the global structure of gravity theories.

Abstract

A kind of topological field theory is proposed as a candidate to describe the global structure of the 2-form Einstein gravity with or without a cosmological constant. Indeed in the former case, we show that a quantum state in the candidate gives an exact solution of the Wheeler-DeWitt equation. The BRST quantization based on the Batalin-Fradkin-Vilkovisky (BFV) formalism is carried out for this topological version of the 2-form Einstein gravity.