Dualities

The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond (2+1)D. It constitutes an exact correspondence that can be understood both as a framework and as a 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 . This opens the door to a new realm of topological phases both in lattice and continuum and across dimensions.