Chern-Simons approach to three-manifold invariants

TL;DR

This paper introduces a novel, non-combinatorial method for computing three-manifold invariants using Chern-Simons theory, providing a direct quantum field theory approach and explicit results for SU(2).

Contribution

It presents a new formal framework for three-manifold invariants via non-perturbative Chern-Simons theory, extending previous combinatorial methods.

Findings

Develops a non-combinatorial approach to invariants

Provides a direct quantum field theory implementation of surgery

Derives explicit form for SU(2) invariants

Abstract

A new, formal, non-combinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of non-perturbative topological quantum Chern-Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is derived.