On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

26 Chapter 1. Introduction: Problems beyond the Standard Model
where the 5D curvature, derived from GMN, and the 4D curvature, derived from the
4D block of GMN, gµν = e −2σ ηµν, are related by R5(G) = e 2σ(φ) R4(g) + . . . up to
terms which vanish upon φ-integration or cancel with cosmological constant terms.
Matching with the 4D Einstein-Hilbert action implies that
M 2 Pl = M 3 Pl(5)
k
�
1 − e −2krcπ�
, (1.53)
which, as a consequence of the strong curvature, is largely independent of the radius
rc, in contrast to (1.47). Likewise, the masses of the KK excitations are not tied to
the radius of the extra dimension, but depend on the curvature scale mn ∼ nMKK,
where
MKK ≡ ke krcπ = k ΛIR
ΛUV
. (1.54)
The observation, that (1.53) is not sensitive to the limit rc → ∞ led to a subsequent
paper of Randall and Sundrum, in which they proposed a model with an infinite
warped extra dimension as an alternative to compactification [56].
Equation (1.50) suggests, that solving the hierarchy problem only require the Higgs
to stay at the IR brane. The conclusions are not altered if all other SM fields are
promoted to bulk fields, which was explored soon after the original paper for bulk
gauge bosons in [57], and bulk fermions in [58, 59]. Similar to the split fermion idea
in UED, a localization in the bulk will lead to a suppression of dangerous higher
dimensional operators, because the overlaps of the extra dimensional wavefunctions
determine the size of the couplings. Due to the warping it can also accommodate
hierarchical fermion masses and mixings coming from anarchic 5D Yukawa couplings,
as well as a suppression of tree-level flavor violating effects. These features will be
elaborated on in Section 2.4 and 2.5.
In the context of the AdS/CFT duality, it can be motivated, that the RS model
is dual to a strong interacting four dimensional theory, see Section 2.2. Therefore,
many concepts introduced in Section 1.1 have an alternative, so called holographic
5D description, which may at first glance look like an entirely different theory. So
is for example the warped higgsless model dual to a walking TC theory [63]. The
warped version of a gauge-Higgs unification model is a dual description of a composite
pseudo-Nambu Goldstone Higgs 19 [62, Sec.4] and the mechanism of collective
symmetry breaking can be implemented by an enlarged bulk gauge group [60].
It is interesting to note, that this dual description for the RS scenario, where gravity is
in the bulk and the graviton can therefore be understood as a composite of the brane
Yang-Mills theory seemingly contradicts a no-go theorem, the Weinberg-Witten theorem
[79]. It states among other things, that a massless graviton cannot be a composite
state. Very reminiscent of the Coleman-Mandula theorem and SUSY, the AdS/CFT
correspondence makes use of a loophole, because the 5D graviton can be described by
a composite state on the four dimensional boundary, see [80] for details.
19 An indication of this relation may be that the extra-dimensional components of the gauge fields
transforms under the 5D gauge symmetry like under a shift symmetry.