“Old” conformal bootstrap on AdS: O(N) symmetric scalar model

Abstract

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh formalism is used in AdS/CFT instead of conventional Feynman-Witten diagrams technique, permits to calculate values of conformal dimensions in the O(N) symmetric model with conformal or composite Habbard-Stratonovich field.

Spinor vertices and bubbles in the old conformal bootstrap in AdS/CFT and the fermion mass hierarchy problem: The Yukawa model

“…Whereas D (1) is derived in Appendix, it will be used in calculation of spinor-spinor-scalar vertex of type II in subsection 3.2:…”

“…There are relations between coefficients d (0) and d (1) that permit significantly simplify the calculations:…”

“…Surely (1) has a tower of solutions beginning from the electro-weak scale L −1 . But it also has a special solution when both arguments of Bessel functions in (1) are small:…”

“…One of the candidates for the theory capable to fix masses of bulk fields may be the "old" conformal bootstrap in the AdS/CFT context [1], [2]. "Old" conformal bootstrap was proposed about 50 years ago in pioneer papers [14], [15] and developed in [16] - [21] (see e.g.…”

“…In the AdS/CFT context finding of conformal dimensions is equivalent to finding of bulk masses. In [1] the values of bulk masses of scalar fields that are the roots of corresponding bootstrap spectral equations were found in certain models under the oversimplifying assumption of replacing of two "intermediate" Green functions in self-energy Witten diagrams (bubbles) by their harmonic counterparts. In [2] this assumption was abandoned, and UV divergence of the bubble was renormalized in the "double-trace from UV to IR flow" way used earlier in calculations of the UV-finite tadpoles and bulk vacuum quantum energies of scalar [23]- [28] and spinor [29]- [30] bulk fields.…”