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2020

Paulos, Miguel F.

We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line.

The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on the crossing equation.
The dispersion relations provide an equivalent formulation of the constraints of the Polyakov bootstrap and hence of crossing symmetry on the line.
The built in positivity properties imply simple and exact lower and upper bounds on the values of general CFT correlators on the Euclidean section, which are saturated by generalized free fields.