A note on universality in refined Chern-Simons theory

TL;DR

This paper explores different refinements of Vogel's universality in Chern-Simons theory, highlighting that the refined version is limited to simply laced Lie groups, unlike the original universal form.

Contribution

It introduces and discusses various refinements of Vogel's universality, emphasizing the restriction to simply laced Lie groups in the refined context.

Findings

Refined Vogel's universality applies only to simply laced Lie groups.

Original universality applies to all simple Lie groups.

Refinement restricts the universality to a subset of Lie groups.

Abstract

We discuss various forms of refinements of Vogel's universality in Chern-Simons theory. While the original universality applies to arbitrary simple Lie groups, its counterpart in refined Chyrn-Simons theory is restricted to simply laced Lie groups.