The Physics Inside Topological Quantum Field Theories

TL;DR

This paper demonstrates how equations of motion in a specialized field space can be represented as operator conditions in a generalized Floer theory, applying this to derive Einstein's equations within a five-dimensional topological quantum field theory.

Contribution

It introduces a novel approach linking equations of motion to operator conditions in Floer theory and applies it to derive Einstein's equations from a topological quantum field theory framework.

Findings

Equations of motion can be realized as operator conditions in Floer theory.

Ghost fields in this construction are non-dynamical.

Einstein's equations are obtained via surgery in a 5D topological quantum field theory.

Abstract

We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a construction are found not to be dynamical. This construction is applied to gravity on a four dimensional manifold, $M$; whereupon, we obtain Einstein's equations via surgery, along $M$, in a five-dimensional topological quantum field theory.