A basis of analytic functionals for CFTs in general dimension

A bstract We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary (for, say, s - and t -channel expansions) can be thought of as vector infinite-dimensional space complex functions two variables, which satisfy boundedness condition at infinity. identify useful basis this functions, consisting set s- t-channel conformal blocks double-twist operators mean field theory. describe independent algorithms construct dual linear functionals, work out explicitly many examples. Our functionals appears closely related CFT dispersion relation recently derived by Carmi Caron-Huot.