Knots and Matrix Models

TL;DR

This paper explores a matrix model with multiple matrices and demonstrates its connection to knot diagrams in a specific limit, also discussing implications for matrix string theory and M(atrix) theory.

Contribution

It introduces a novel matrix model framework that relates to knot diagrams and discusses its potential relevance to M(atrix) theory and string theory.

Findings

Matrix model with d matrices describes knot diagrams at large N and d=0.

Connection established between matrix models and knot theory.

Speculation on the existence of a fundamental M(atrix) in void.

Abstract

We consider a matrix model with d matrices NxN and show that in the limit of large N and d=0 the model describes the knot diagrams. The same limit in matrix string theory is also discussed. We speculate that a prototypical M(atrix) without matrix theory exists in void.