A Relation Between Topological Quantum Field Theory and the Kodama State

TL;DR

This paper explores the connection between topological quantum field theory and the Kodama state, revealing that the latter represents a topological state with unbroken diffeomorphism invariance in Yang-Mills and general relativity.

Contribution

It demonstrates that the Kodama (Chern-Simons) state corresponds to a topological state with unbroken diffeomorphism invariance, providing a clear explanation for its existence.

Findings

Kodama state describes a topological state with unbroken diffeomorphism invariance.

Establishes a relation between topological quantum field theory and the Kodama state.

Provides an explanation for the existence of such topological states.

Abstract

We study a relation between topological quantum field theory and the Kodama (Chern-Simons) state. It is shown that the Kodama (Chern-Simons) state describes a topological state with unbroken diffeomorphism invariance in Yang-Mills theory and Einstein's general relativity in four dimensions. We give a clear explanation of "why" such a topological state exists.