Knot theory and a physical state of quantum gravity

TL;DR

This paper explores the connection between knot theory and quantum gravity, focusing on how knot invariants relate to the loop representation of quantum gravity and discussing the Kodama wavefunction as a potential ground state.

Contribution

It provides a comprehensive review linking knot invariants to loop quantum gravity and introduces the Kodama wavefunction as a candidate for the gravitational ground state.

Findings

Knot invariants naturally arise in gravitational physics

The Kodama wavefunction is a conjectured ground state of quantum gravity with positive cosmological constant

The paper offers an accessible introduction to loop quantum gravity for diverse audiences

Abstract

We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative canonical quantum general relativity (loop quantum gravity). This leads naturally to a discussion of the Kodama wavefunction, a state which is conjectured to be the ground state of the gravitational field with positive cosmological constant. This review can serve as a self-contained introduction to loop quantum gravity and related areas. Our intent is to make the paper accessible to a wider audience that may include topologists, knot-theorists, and other persons innocent of the physical background to this approach to quantum gravity.