The relation between braid and exclusion statistics is examined in onedimensional
systems, within the framework of Chern–Simons statistical
transmutation in gauge invariant form with an appropriate dimensional
reduction. If the matter action is anomalous, as for chiral fermions, a relation
between braid and exclusion statistics can be established explicitly for both
mutual and nonmutual cases. However, if it is not anomalous, the exclusion
statistics of emergent low energy excitations is not necessarily connected to
the braid statistics of the physical charged fields of the system. Finally, we
also discuss the bosonization of one-dimensional anyonic systems through
T-duality
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