Anyonic correlation functions 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 $2\to 2$ 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.

arXiv comment23 pages, v2 : Subsection 5.4 on $⟨TTTT⟩$ added. Added details of the strategy employed in Section 4. v3 : version accepted in PRD

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• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• The Hilbert Space of large $N$ Chern-Simons matter theories
• 4D Flat-space scattering amplitude /$CF{T}_3$ correlator correspondence revisited