Fermionization and Convergent Perturbation Expansions in Chern-Simons Gauge Theory

We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to conjecture that Chern-Simons gauge theory also gives rise to convergent perturbation expansions, which would give a mathematically well-defined construction of the theory.