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Construction of topological field theories using BV
We discuss in detail the construction of topological field theories using the
Batalin--Vilkovisky (BV) quantisation scheme. By carefully examining the
dependence of the antibracket on an external metric, we show that
differentiating with respect to the metric and the BRST charge do not commute
in general. We introduce the energy momentum tensor in this scheme and show
that it is BRST invariant, both for the classical and quantum BRST operators.
It is antifield dependent, guaranteeing gauge independence. For topological
field theories, this energy momentum has to be quantum BRST exact. This leads
to conditions at each order in . As an example of this procedure, we
consider topological Yang--Mills theory. We show how the reducible set of
symmetries used in topological Yang--Mills can be recovered by means of trivial
systems and canonical transformations. Self duality of the antighosts is
properly treated by introducing an infinite tower of auxiliary fields. Finally,
it is shown that the full energy momentum tensor is classically BRST exact in
the antibracket sense.Comment: 15