New Skins for an Old Ceremony: The Conformal Bootstrap and the Ising Model
by
Sheer El-Showk(IPhT Saclay, France)
→
Europe/Stockholm
122:026
122:026
Description
The existence of a positive linear functional acting on the space of
(differences between) conformal blocks has been shown to rule out
regions in the parameter space of conformal field theories (CFTs). We
argue that at the boundary of the allowed region the extremal functional
contains, in principle, enough information to determine the dimensions
and OPE coefficients of an infinite number of operators appearing in the
correlator under analysis. Based on this idea we develop the Extremal
Functional Method (EFM), a numerical procedure for deriving the spectrum
and OPE coefficients of CFTs lying on the boundary
(of solution space). We test the EFM by using it to rederive the low
lying spectrum and OPE coefficients of the 2d Ising model based solely
on the dimension of a single scalar quasi-primary – no Virasoro algebra
required. Our work serves as a benchmark for applications to more
interesting, less known CFTs (such as the 3d Ising model) in the near
future.
