On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

2 The Randall Sundrum
Model and its Holographic
Interpretation
The model considered in this thesis is a variation of the Randall-Sundrum (RS) model
presented in Section 1.1. This model is enormously rich what concepts of model
building is concerned. Following the original motivation [55], it can be understood
as an extra dimensional theory with an Anti de Sitter metric in continuation of the
idea of large extra dimensions. This point of view will be introduced in Section 2.1.
It is also a model of strongly coupled composite fields, which becomes apparent in
the light of the AdS/CFT correspondence, which will be comprehensively presented
in Section 2.2. In the specific realization of the RS model that forms the basis of this
thesis, all standard model fermions and gauge bosons are five dimensional fields, or
in the language of the strongly coupled description, have composite admixtures (in a
generalization of ρ photon mixing). The technical aspects of this field content will be
the subject of Sections 2.3 and 2.4. Based on this setup and even more important in
the context of the following chapters, the Randall-Sundrum model provides one of the
best explanations for the Flavor structure in the SM we have today. The hierarchies in
quark masses and mixing angles can be reproduced and associated therewith, FCNCs
from higher dimensional operators are suppressed. In Section 2.5 will be explained how
this works and the connection with the concept of partial compositeness as introduced
in Section 1.1 will be established.
2.1 Why this and not that?
The geometrical setup of the RS model has already been introduced in Section 1.1.
This section serves to describe the motivation for this particular geometry and the
choice of localization of the SM fields (whether they are bulk fields or why they should
be confined to one brane or the other).
On first sight, the metric in (1.49) seems to be constructed and the question arises if
it corresponds to a generic approach to assume such a metric or if it is based on very
special assumptions. In other words, is there some hidden tuning like in the case of
large extra dimensions in the specific choice of the geometry?
In order to check this, we will make the most general ansatz compatible with 4D
Poincaré invariance and the Z2 orbifold symmetry, 1
ds 2 = GMNdx M dx N = a(φ) ηµνdx µ dx ν − b(φ) dφ 2 . (2.1)
1 Remember, that the orbifold is a necessity if one wants to describe chiral fermions in an odd
number of spacetime dimensions.