  The composite particle duality extends the notions of both flux attachment
and statistical transmutation in spacetime dimensions beyond 2+1$\text{D}$. It
constitutes an exact correspondence that can be understood either as a
theoretical framework or as a dynamical physical mechanism. The immediate
implication of the duality is that an interacting quantum system in arbitrary
dimensions can experience a modification of its statistical properties if
coupled to a certain gauge field. In other words, commutation relations of
quantum fields can be effectively modified by a dynamical physical process. For
instance, an originally bosonic quantum fluid in d spatial dimensions can
feature composite fermionic (or anyonic) excitations when coupled to a
statistical gauge field. We compute the explicit form of the aforementioned
synthetic gauge fields in $\text{D} \le 3 + 1$. This opens the door to a new
realm of topological phases across dimensions both in lattice and continuum
systems.
