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arXiv · 2312.13344

Improving the five-point bootstrap

David Poland·Valentina Prilepina·Petar Tadić
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Abstract

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Pad\'e approximant to accelerate its convergence. We then study the $\langle\sigma\sigma\epsilon\sigma\sigma\rangle$ correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff $\Delta\leqslant \Delta_{\rm cutoff}$. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

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David Poland, Valentina Prilepina, Petar Tadić. 2023-12-20. Improving the five-point bootstrap. https://doi.org/10.1007/jhep05(2024)299

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