Reshetikhin-Turaev construction and $\mathrm{U}(1)^n$ Chern-Simons partition function

TL;DR

This paper establishes a connection between $ ext{U}(1)^n$ Chern-Simons partition functions and Reshetikhin-Turaev invariants, revealing that the latter are derived from a twisted category rather than a modular one, and extending Chern-Simons duality to these invariants.

Contribution

It demonstrates that Reshetikhin-Turaev invariants in the abelian case are constructed from a twisted category, extending Chern-Simons duality to these invariants.

Findings

Reshetikhin-Turaev invariants relate to $ ext{U}(1)^n$ Chern-Simons partition functions

Construction relies on a twisted category, not a modular one

Chern-Simons duality extends to Reshetikhin-Turaev invariants

Abstract

In this article, we show that the $\mathrm{U}(1)^n$ Chern-Simons partition functions are related to Reshetikhin-Turaev invariants. In this abelian context, it turns out that the Reshetikhin-Turaev construction that yields these invariants relies on a ``twisted" category rather than a modular one. Furthermore, the Chern-Simons duality of the $\mathrm{U}(1)^n$ partition functions straightforwardly extend to the corresponding Reshetikhin-Turaev invariants.