Torus Knot and Minimal Model

TL;DR

This paper uncovers a deep link between quantum knot invariants for torus knots and the characters of minimal models in conformal field theory, showing that Kashaev's invariant matches Eichler integrals of these characters.

Contribution

It establishes a novel connection between quantum knot invariants and minimal model characters, bridging knot theory and conformal field theory.

Findings

Kashaev's invariant equals Eichler integral of minimal model character

Quantum invariants for torus knots relate to conformal field theory

Provides a new perspective on knot invariants through minimal models

Abstract

We reveal an intimate connection between the quantum knot invariant for torus knot T(s,t) and the character of the minimal model M(s,t), where s and t are relatively prime integers. We show that Kashaev's invariant, i.e., the N-colored Jones polynomial at the N-th root of unity, coincides with the Eichler integral of the character.