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Instanton Dynamics in the Broken Phase of the Topological Sigma Model
The topological model with the black hole metric of the target space
is considered. It has been shown before that this model is in the phase with
BRST-symmetry broken. In particular, vacuum energy is non-\-zero and
correlation functions of observables show the coordinate dependence. However
these quantities turned out to be infrared (IR) divergent. It is shown here
that IR divergences disappear after the sum over an arbitrary number of
additional instanton-\-anti-\-instanton pairs is performed. The model appears
to be equivalent to Coulomb gas/Sine Gordon system.Comment: some references added
The Broken Phase of the Topological Sigma model
The topological sigma model with the semi-infinite cigar-like target space
(black hole geometry) is considered. The model is shown to possess unsuppressed
instantons. The noncompactness of the moduli space of these instantons is
responsible for an unusual physics. There is a stable vacuum state in which the
vacuum energy is zero, correlation functions are numbers thus the model is in
the topological phase. However, there are other vacuum states in which
correlation functions show the coordinate dependence. The estimation of the
vacuum energy indicates that it is nonzero. These states are interpreted as the
ones with broken BRST-symmetry.Comment: 30 pages, LATE
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