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arXiv · 0706.1533

Renormalisation and the Batalin-Vilkovisky formalism

Kevin J. Costello
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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.

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Kevin J. Costello. 2007-06-29. Renormalisation and the Batalin-Vilkovisky formalism. https://arxiv.org/abs/0706.1533

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