On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots

TL;DR

This paper explores unexpected connections between Jones' subfactor theory, conformal field theory, Thompson's groups, and knot theory, revealing new insights in mathematical physics.

Contribution

It uncovers novel links between subfactors, Thompson's groups, and knots, inspired by an accidental discovery in quantum field theory.

Findings

Thompson's groups relate to subfactor theory and knot invariants

New mathematical structures emerge from quantum field theory insights

Potential applications in understanding quantum symmetries

Abstract

Surprisingly Richard Thompson's groups have recently appeared in Jones' subfactor theory. Vaughan Jones is famous for linking theories that are a priori completely disconnected; for instance, his celebrated polynomial for links emanating from subfactor theory. This note is about a new beautiful story in mathematics which results from a fortunate accident in the land of quantum field theory.