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.

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

References in corpus (18)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Conformal collider physics: Energy and charge correlations
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Higher Spins in AdS and Twistorial Holography
• Local bulk S-matrix elements and CFT singularities
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Landau diagrams in AdS and S-matrices from conformal correlators
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• A Derivation of AdS/CFT for Vector Models
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Momentum space parity-odd CFT 3-point functions
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Helicity basis for three-dimensional conformal field theory
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound
• Four point functions in CFT's with slightly broken higher spin symmetry
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle

Cited by in corpus (9)

• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• 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