Anyonic correlation functions in Chern-Simons matter theories

TL;DR

This paper derives three-point correlation functions in 3d Chern-Simons matter theories, revealing a relation to free theories and introducing an anyonic phase that interpolates between free fermion and boson results, consistent with duality.

Contribution

It introduces a novel relation between parity even and odd correlator parts, enabling the calculation of 3-point functions from free theories and incorporating an anyonic phase in large N theories.

Findings

Correlation functions interpolate between free fermion and boson theories.

The anyonic phase matches previous S-matrix results and respects duality.

Explicit formulas for correlators in Chern-Simons matter theories.

Abstract

Using a novel relation between the parity even and odd parts of a correlator, we show that the 3-point function of conserved or weakly broken currents in 3d 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 $2\rightarrow 2$ 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.