Bootstrapping CFTs with the Extremal Functional Method

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 in the near
future, such as the 3d Ising model.

Event Type: 
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Event Date: 
Tuesday, November 27, 2012 - 14:00 to 15:30
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