Perturbing Topological Field Theories

TL;DR

This paper demonstrates that local gauge-invariant perturbations in abelian Chern-Simons theory do not alter the correlation functions of Wilson lines, confirming the stability of the linking number under such perturbations.

Contribution

It provides a detailed four-loop calculation showing the invariance of Wilson line correlators in perturbed abelian Chern-Simons theory, highlighting the robustness of topological invariants.

Findings

Correlation functions unaffected by perturbations up to four loops

Linking number remains stable under local gauge-invariant modifications

Perturbations do not alter topological invariants in abelian Chern-Simons theory

Abstract

The abelian Chern-Simons theory is perturbed by introducing local gauge-invariant interaction terms depending on the curvature. The computation of the correlation function of two Wilson lines for two smooth closed nonintersecting curves is reported up to four loops and is shown to be unaffected by radiative corrections. This result ensures the stability of the linking number of the two curves with respect to the local perturbations which may be added to the Chern-Simons action.