  We address nonperturbative dynamics of the two-dimensional bosonic and
supersymmetric $\mathbb{C}P^{N-1}$ models for general $N$ by developing new
tools directly on $\mathbb{R}^2$. The analysis starts with a new formulation of
instantons that is consistent with the existence of the classical moduli space,
classical dipole--dipole type interactions of instanton--anti-instanton pairs,
and vanishing interaction of instanton--instanton pairs. The classical
consistency is achieved via a representation of the instanton as a collection
of $N$ pointlike constituents carrying pair of real and imaginary charges
valued in the weight lattice of $SU(N)$. The constituents interact via a
generalized Coulomb interaction and do not violate the fact that instanton is a
single lump with integer topological charge. By developing the appropriate
Gibbs distribution, we show that the vacuum can be captured by a statistical
field theory of these constituents, and their cluster expansion. Contrary to
the common belief that instantons do not capture the vacuum structure and
non-perturbation properties of such theories, our refined analysis is able to
produce properties such as mass gap, theta dependence, and confinement of the
theory on $\mathbb{R}^2$. In supersymmetric theory, our construction gives a
new derivation of the mirror symmetry between the sigma model and the dual
Landau--Ginzburg model by Hori and Vafa. Our construction also demonstrates
that there is absolutely no conflict between large $N$ and instantons.
