Spinor vertexes and bubbles in the "old" conformal bootstrap on AdS and FMH problem: Yukawa model

TL;DR

This paper extends the old conformal bootstrap approach in AdS to calculate bulk fermion masses, deriving simple expressions for spinor-scalar interactions and spectral equations in the Yukawa model, addressing the Fermion mass hierarchy problem.

Contribution

It introduces a method to compute bulk fermion masses in AdS using the conformal bootstrap, including new calculations of spinor-scalar vertices and bubbles, and applies this to the Yukawa model.

Findings

Derived simple formulas for spinor-scalar bubbles.

Established spectral equations for bulk fermion masses.

Applied the approach to the SU(N) Yukawa model in 4D.

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 the "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. Calculation of spinor-scalar vertices is performed in physical AdS space, and unexpectedly simple expressions for spinor-scalar bubbles (2-point one-loop self-energy Witten diagrams) are obtained. The "double-trace from UV to IR flow" subtraction of UV divergences used earlier in calculations of the UV-finite bulk tadpoles is applied to bubbles. This permitted to write down in frame of the "old" conformal bootstrap approach the nontrivial spectral equations for the bulk fermion masses; SU(N) Yukawa model of spinor fields interacting with conformal invariant scalar field in case of four boundary dimensions is considered as a specific example.