Abstract:
In recent years, there has been renewed interest in the conformal
bootstrap program, which uses crossing symmetry to constrain the data
of unitary conformal field theories (in any dimension) by comparing
different channels in which one can  evaluate a four-point function.
Most of the progress so far has been for four-point functions of
scalar operators.  I will review those constructions and discuss their
limitations, explaining why we should be interested in non-scalar
operators.  Then I will explain how to construct all the ingredients
needed to set up the next natural example: a four-point function of
two scalars and two vectors.