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

TL;DR

This paper applies UV-finite conformal bootstrap techniques to scalar models in AdS, deriving simple expressions for bubble diagrams and analyzing spectral roots within unitarity bounds in four-dimensional boundary space.

Contribution

It extends UV-finite conformal bootstrap methods to AdS scalar models, providing explicit formulas for bubble diagrams and spectral roots in four dimensions.

Findings

Derived simple expressions for bubble self-energy diagrams in AdS.

Identified three spectral roots satisfying unitarity bounds for each N in O(N) models.

Extended the conformal bootstrap approach to UV-finite calculations in AdS.

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.