Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory

Abstract

We compute the two, three point function of the opearators in the spin zero multiplet of $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory at large $N$ and at all orders of 't Hooft coupling by solving the Schwinger-Dyson equation. Schwinger-Dyson method to compute four point function becomes extremely complicated and hence we use bootstrap method to solve for four point function of scaler operator $J_0^f=\bar{\psi }\psi$ and $J_0^b=\bar{\varphi }\varphi$. Interestingly, due to the fact that $⟨J_0^f{J}_0^f{J}_0^b⟩$ is a contact term, the four point function of $J_0^f$ operator looks like that of free theory up to overall coupling constant dependent factors and up to some bulk AdS contact terms. On the other hand the $J_0^b$ four-point function receives an additional contribution compared to the free theory expression due to the $J_0^f$ exchange. Interestingly, double discontinuity of this single trace operator $J_0^f$ vanishes and hence it only contributes to AdS-contact term.

19+15 pages, 6 appendices, 7 figures

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• 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
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• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Superconformal invariants and spinning correlators in 3d $\mathcal{N}=2$ SCFTs
• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT