The five-point bootstrap

David Poland; Valentina Prilepina; Petar Tadić

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arXiv · 2305.08914

The five-point bootstrap

David Poland·Valentina Prilepina·Petar Tadić

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Abstract

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators $\langle \sigma \sigma \epsilon \sigma \sigma \rangle$ in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff $\Delta \leqslant \Delta_{\rm cutoff}$. We then compute several OPE coefficients involving $\epsilon$ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

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David Poland, Valentina Prilepina, Petar Tadić. 2023-05-15. The five-point bootstrap. https://arxiv.org/abs/2305.08914

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