  This is a brief summary of our studies of quantum field theories in a special
limit in which the instantons are present, the anti-instantons are absent, and
the perturbative corrections are reduced to one-loop. We analyze the
corresponding models as full-fledged quantum field theories, beyond their
topological sector. We show that the correlation functions of all, not only
topological (or BPS), observables may be studied explicitly in these models,
and the spectrum may be computed exactly. An interesting feature is that the
Hamiltonian is not always diagonalizable, but may have Jordan blocks, which
leads to the appearance of logarithms in the correlation functions. We also
find that in the models defined on Kahler manifolds the space of states
exhibits holomorphic factorization. In particular, in dimensions two and four
our theories are logarithmic conformal field theories.
