Renormalisation and the Batalin-Vilkovisky formalism

Details Renormalisation and the Batalin-Vilkovisky formalism Renormalisation and the Batalin-Vilkovisky formalism

2007-06-11

arxiv.org/abs/0706.1533v3

Mathematics

Quantum Algebra

88 pages

Scientific paper

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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