Knot invariants from rational conformal field theories

TL;DR

This paper develops a general framework for deriving knot and link invariants from rational conformal field theories, extending previous Chern-Simons-based approaches to include various models like minimal, superconformal, and W_N models.

Contribution

It introduces a unified method to obtain knot invariants from rational conformal field theories, broadening the scope beyond Chern-Simons theories.

Findings

Relates invariants from conformal field theories to those from Wess-Zumino models.

Suggests possible Chern-Simons representations for these models.

Generalizes earlier knot invariant constructions from Chern-Simons theories.

Abstract

A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ models are studied. The invariants are related to the invariants obtained from the Wess-Zumino models associated with the coset representations of these models. Possible Chern-Simons representation of these models is also indicated. This generalises the earlier work on knot and link invariants from Chern-Simons theories.