Renormalisation and the Batalin-Vilkovisky formalism
Quantum Algebra
2007-06-29 v3 High Energy Physics - Theory
Abstract
This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renormalised in a way respecting all symmetries (up to homotopy). This yields an invariant of smooth manifolds: a certain algebraic structure on the cohomology of the manifold tensored with a Lie algebra, which is a "higher loop" enrichment of the natural Lie-infinity structure.
Cite
@article{arxiv.0706.1533,
title = {Renormalisation and the Batalin-Vilkovisky formalism},
author = {Kevin J. Costello},
journal= {arXiv preprint arXiv:0706.1533},
year = {2007}
}