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- 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.

Collection/Series:

Event Type:

Seminar

Scientific Area(s):

Speaker(s):

Event Date:

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

Location:

Time Room

©2012 Perimeter Institute for Theoretical Physics