Knot Physics on Entangled Vortex-Membranes: Classification, Dynamics and Effective Theory

TL;DR

This paper explores the physics of entangled vortex-membranes called composite knot-crystals, deriving effective quantum field theories and gauge interactions, potentially offering an alternative view of quantum field theory through knot dynamics.

Contribution

It introduces a classification and effective theory for knot physics on vortex-membranes, connecting topological structures to quantum field theories and the Standard Model.

Findings

Effective theories of coupled zero-lattices become quantum field theories.

Gauge interactions emerge from topological interplay.

Derived the Standard Model from a specific knot-crystal configuration.

Abstract

In this paper, knot physics on entangled vortex-membranes are studied including classification, knot dynamics and effective theory. The physics objects in this paper are entangled vortex-membranes that are called composite knot-crystals. Under projection, a composite knot-crystal is reduced into coupled zero-lattices. In the continuum limit, the effective theories of coupled zero-lattices become quantum field theories. After considering the topological interplay between knots and different types of zero-lattices, gauge interactions emerge. Based on a particular composite knot-crystal with (N=4, M=3) (we call it standard knot-crystal), the derived effective model becomes the (one-flavor) Standard model. As a result, the knot physics may provide an alternative interpretation on quantum field theory.