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.
Highlights
Explaining the fermion mass hierarchy remains a challenge in theoretical physics
In frames of the anti-de Sitter (AdS)=CFT approach and two-branes Randall-Sundrum model [4] (Poincarecoordinate ε < z < L where ε−1 ∼ MPl 1⁄4 1019 GeV for the Planck scale and L−1 ∼ MEW 1⁄4 102 GeV for the electroweak scale), spectra of physical particles are obtained as eigenvalues of equations for bulk fields, and it is possible in principle to get the lookedfor fermion masses of intermediate scales with the choice of dynamics in the bulk and of boundary conditions on both branes [5,6,7,8,9]
In Ref. [12], 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’s functions in selfenergy Witten diagrams by their harmonic counterparts
Summary
Explaining the fermion mass hierarchy ( called the flavor hierarchy problem) remains a challenge in theoretical physics (see, e.g., Refs. [1,2] and references therein). [12], 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’s functions in selfenergy Witten diagrams (bubbles) by their harmonic counterparts. The tool is simple, it says that, instead of ordinary Witten diagrams, the difference of two similar Witten diagrams built of UV and IR bulk Green’s functions must be considered This difference is the deformation in amplitudes under double-trace flow from UV to IR boundary conditions, as was first proposed in Ref. The Conclusion sums up three principle results of the paper and outlines the possible directions of future work
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