Improving the five-point bootstrap
David Poland, Valentina Prilepina, Petar Tadić
Abstract
A bstract 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 〈 σσϵσσ 〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆ 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.