Localization and non-renormalization in Chern-Simons theory

Abstract

We revisit and clarify some aspects of perturbative renormalization in pure Chern-Simons theory by means of a localization principle associated with an underlying supersymmetry. This perspective allows the otherwise perturbative one-loop shifts to be interpreted as nonperturbative consequences of a non-renormalization theorem, while providing a unified understanding of their origin (particularly in the case of Wilson lines). We illustrate this approach explicitly for SU(2) Chern-Simons theory in flat space, on Seifert manifolds, and on a solid torus.