Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.
A note on the analyticity of AdS scalar exchange graphs in the crossed channel
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We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.
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A thermal representation for conformal ladder integrals
Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.