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

Abstract

Attempts to resolve the longstanding Fermion mass hierarchy (FMH) problem in frames of the AdS/CFT correspondence demand the knowledge of bulk fermion masses. The approach of "old" conformal bootstrap in AdS context permitted to calculate bulk masses of scalar fields [1], [2]. In the present paper this approach is extended to physically more interesting spin 1/2 bulk fields. The unexpectedly simple expressions for spinor-scalar bubbles (2-point one-loop self-energy Witten diagrams) are obtained with application of the "double-trace from UV to IR flow" regularization used earlier in calculations of the UV-finite bulk tadpoles. In case of four boundary dimensions the nontrivial spectral equations for bulk fermion masses are written down in the SU(N) Yukawa model of spinor fields interacting with conformal invariant scalar field. Calculating the roots of these and similar bootstrap equations is a task for future.