Using a novel relation between the parity-even and -odd parts of a correlator, we show that the three-point function of conserved or weakly broken currents in three-dimensional conformal field theory (CFT) can be obtained from just the free fermion (FF) or the free boson (FB) theory. In the special case of large $N$ Chern-Simons matter theories, we obtain the correlator in terms of a coupling constant dependent “anyonic phase” factor. This anyonic phase factor was previously obtained in the $2\to 2$ exact S-matrix result and is consistent with strong-weak duality. By varying the coupling constant, the CFT correlator interpolates nicely between the same in the FF and FB theories.

• Received 26 December 2021
• Accepted 8 August 2022

DOI:https://doi.org/10.1103/PhysRevD.106.046014

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Published by the American Physical Society