Improving the five-point bootstrap

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 Padé approximant to accelerate its convergence. We then study the $⟨\sigma \sigma \epsilon \sigma \sigma ⟩$ correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff $\Delta ⩽{\Delta }_{\mathrm{cutoff}}$. 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.

27 pages, 1 attached Mathematica notebook, v2: minor error fixed, v3: small adjustments, v4: typo fixed and small adjustment

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Cited by in corpus (7)

• Bootstrapping the 3d Ising Stress Tensor
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• The thermal bootstrap for the critical O(N) model
• Wilson Loops with Lagrangians: Large Spin OPE and Cusp Anomalous Dimension Dictionary
• Sparsity in the numerical six-point bootstrap
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class