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Momentum-space conformal blocks on the light cone
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abstract
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks are polynomials in the cosine of the scattering angle, with degree $\ell$ corresponding to the spin of the intermediate operator. The coefficients of these polynomials are obtained in a closed-form expression for arbitrary spacetime dimension $d > 2$. If the scaling dimension of the intermediate operator is large, the conformal block reduces to a Gegenbauer polynomial $\mathcal{C}_\ell^{(d-2)/2}$. If on the contrary the scaling dimension saturates the unitarity bound, the block is different Gegenbauer polynomial $\mathcal{C}_\ell^{(d-3)/2}$. These results are then used as an inversion formula to compute OPE coefficients in a free theory example.
Forward citations
Cited by 5 Pith papers
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Conformal 3-point functions and the Lorentzian OPE in momentum space
The paper derives a closed Appell F4 expression for the Wightman 3-point function of scalar operators and for two scalars with one traceless symmetric tensor in Lorentzian momentum space.
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Lorentzian CFT 3-point functions in momentum space
Lorentzian CFT three-point functions in momentum space are derived in arbitrary dimensions for scalars and for one energy-momentum tensor with two scalars, with an application to ANEC expectation values.
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Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension
The authors extend their momentum-space Polyakov block construction for scalar conformal four-point functions from three dimensions to general spacetime dimension d, with explicit formulas for arbitrary-spin exchanges.
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Towards the higher point holographic momentum space amplitudes II: Gravitons
A method that expresses AdS4 graviton Witten diagrams as a differential operator acting on one scalar factor, with explicit three, four, and five point results.
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Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory
Lecture notes recapping off-shell spinor helicity, twistor, and super-twistor methods for 3d CFT correlators, with 55 exercises and no substantial new research result.
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