Description
In this talk, I will present a practical realization of the higher-point conformal
bootstrap, focusing on the five-point comb channel implementation thereof. I
will consider 5-point scalar correlators in d-dimensional conformal field theories
(CFTs). I will begin by laying out a robust algorithm for the efficient numeri-
cal evaluation of conformal blocks for exchanged primary operators of arbitrary spin. I will then describe an explicit implementation of the 5-point bootstrap.
With this, I will proceed to study 5-point correlators in the 3d critical Ising model. I will examine correlators involving \sigma, and \epsilon, truncating the oper-ator product expansion (OPE) to include contributions due to operators with
conformal dimension below a certain cutoff. In each case, I will approximate
the remaining contributions by their counterparts in a suitable disconnected five-point correlator. Finally, I will discuss the results obtained through the five-point
bootstrap for a number of OPE coefficients involving two or more spinning oper-
ators. While these coefficients are nontrivial to access by means of the four-point
bootstrap, they are within ready reach of the higher-point bootstrap, where we
are able to compute a number of OPE coefficients with greater accuracy than
previous methods. I will compare some newly-determined OPE coefficients to
corresponding results from the four-point bootstrap and the fuzzy sphere regu-
larization technique. At the end, I will give a preview of the six-point snowflake
channel implementation of this method. This analysis will ultimately establish
the higher-point bootstrap as a powerful tool for studying CFTs.
