Momentum space spinning correlators and higher spin equations in three dimensions

Abstract

In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the five-point function of the scalar operator in the free bosonic theory. We discuss techniques which are more efficient than the usual PV reduction to evaluate one loop integrals. Our techniques can be easily generalised to momentum space correlators of complicated spinning operators and to higher point functions. The three dimensional fermionic theory has the interesting feature that the scalar operator $\bar{\psi }\psi$ is odd under parity. To account for this, we develop a parity odd basis which is useful to write correlation functions involving spinning operators and an odd number of $\bar{\psi }\psi$ operators. We further study higher spin (HS) equations in momentum space which are algebraic in nature and hence simpler than their position space counterparts. We use them to solve for three-point functions involving spinning operators without invoking conformal invariance. However, at the level of four-point functions, solving the HS equation requires additional constraints that come from conformal invariance and we could only verify that our explicit results solve the HS equation.

arXiv commentTypos fixed, references added, a comment on the scalar five point function in the free fermionic theory removed

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• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
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• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• 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
• Mixed three-point functions of conserved currents in three-dimensional superconformal field theory
• Momentum space CFT correlators of non-conserved spinning operators
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ superconformal field theory
• 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
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• ANEC in $\lambda {\varphi }^4$ theory
• $n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Three-point functions of fermionic higher-spin currents in 4D conformal field theory
• The Conformal Anomaly Action to Fourth Order (4T) in $d=4$ in Momentum Space