  In both Yang-Mills theories and sigma models, instantons are endowed with
degrees of freedom associated to their scale size and orientation. It has long
been conjectured that these degrees of freedom have a dual interpretation as
the positions of partonic constituents of the instanton. These conjectures are
usually framed in d=3+1 and d=1+1 dimensions respectively where the partons are
supposed to be responsible for confinement and other strong coupling phenomena.
We revisit this partonic interpretation of instantons in the context of d=4+1
and d=2+1 dimensions. Here the instantons are particle-like solitons and the
theories are non-renormalizable. We present an explicit and calculable model in
d=2+1 dimensions where the single soliton in the CP^N sigma-model can be shown
to be a multi-particle state whose partons are identified with the ultra-violet
degrees of freedom which render the theory well-defined at high energies. We
introduce a number of methods which reveal the partons inside the soliton,
including deforming the sigma model and a dual version of the Bogomolnyi
equations. We conjecture that partons inside Yang-Mills instantons hold the key
to understanding the ultra-violet completion of five-dimensional gauge
theories.

High Energy Physics - Theory