  From the perspective of topological field theory we explore the physics
beyond instantons. We propose the fluctons as nonperturbative topological
fluctuations of vacuum, from which the self-dual domain of instantons is
attained as a particular case. Invoking the Atiyah-Singer index theorem, we
determine the dimension of the corresponding flucton moduli space, which gives
the number of degrees of freedom of the fluctons. An important consequence of
these results is that the topological phases of vacuum in non-Abelian gauge
theories are not necessarily associated with self-dual fields, but only with
smooth fields. Fluctons in different scenarios are considered, the basic
aspects of the quantum mechanical amplitude for fluctons are discussed, and the
case of gravity is discussed briefly.
