UV-finite 'old' conformal bootstrap on AdS: scalar case

Abstract The double-trace from UV to IR flow subtraction of infinities used earlier for the UV-convergent calculations of the Witten tadpole diagrams being applied to the bubble self-energy diagrams gives for them the amazingly simple expressions in case of the four- dimensional boundary space. For every N = 1 … 4 in the O(N) symmetric scalar fields model with the conformal Hubbard-Stratonovich field there are three roots of the “old” conformal bootstrap spectral equations that obey unitarity bound demand.