Localization and Non-Renormalization in Chern-Simons Theory
arXiv:1805.11076 · doi:10.1007/JHEP01(2019)065
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 Chern-Simons theory in flat space, on Seifert manifolds, and on a solid torus.
62 pages + appendices, comments very welcome; v2: minor improvements (published version is abridged)