The Kodama state for topological quantum field theory beyond instantons

TL;DR

This paper demonstrates that the Kodama (Chern-Simons) state, previously linked only to instantons, actually exists across the entire topological sector of topological Yang-Mills theory, with brief implications for gravity.

Contribution

It extends the understanding of the Kodama state to the full topological sector, beyond instantons, in topological quantum field theories.

Findings

The Kodama state exists for the complete topological sector.

A symplectic structure preserving symmetries and topological invariance is constructed.

Brief discussion on implications for gravity.

Abstract

Constructing a symplectic structure that preserves the ordinary symmetries and the topological invariance for topological Yang-Mills theory, it is shown that the Kodama (Chern-Simons) state traditionally associated with a topological phase of unbroken diffeomorphism invariance for instantons, exists actually for the complete topological sector of the theory. The case of gravity is briefly discussed.