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Renormalisation and the Batalin-Vilkovisky formalism - Costello, Kevin J.
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.