Topological gauge fields and the composite particle duality

We unveil a duality that extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond (2+1)D. Thus, a quantum system in arbitrary dimensions can experience a modification of its statistical properties if coupled to a certain gauge field. For instance, a bosonic quantum fluid 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 D 3 + 1. We introduce a bosonic liquid and its composite dual in (1+1)D as proof of principle. We recover well-known results, resolve old controversies, and suggest a microscopic mechanism for the emergence of such a gauge field. We also outline potential directions for experimental realizations in ultracold atom platforms.