On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

3.5. Implications for Other Theories 123
and the electroweak contributions to C5 in the custodially protected model. However,
the extended color gauge group already cancels the gluon contributions to C5, so that
in the electroweak corrections will reinforce the corrections from this mixed-chirality
operator, with the result of a bound of roughly MKK > 3 TeV.
The right panels in Figure 3.7 show the improvement even clearer as they compare the
percentages of parameter points which fulfill the ɛK constraint in 1 TeV bins of MKK
in the minimal (upper row) or custodially protected (lower row) RS model (blue) and
the corresponding RS model with extended gauge sector (orange). While in the RS
model, less than 5% of parameter points in the lowest bin agree with the constraint
from ɛK roughly 17% (9% with custodial protection) agree in the RS model with an
extended color group.
ff
This RS model with extended color gauge group does therefore not require fine-tuning
in order to agree with the bounds from ∆F = 2 observables, although a tension prevails
if a custodial protection is assumed.
3.5 Implications for Other Theories
In Chapter 2, below equation (2.41) is discussed, how a gauge symmetry in the bulk
of the RS model corresponds to a global symmetry in the composite sector of the
dual theory. This is the starting point for the understanding of the absence of any
contributions to the dangerous Wilson coefficients in (3.20) in the strongly coupled
dual of the RS model with an extended color gauge symmetry. Theories without a
holographic dual (in particular CTC), as described towards the end of Section 1.1
might also evade exclusion if this mechanism is applied.
Let us remind ourselves, that the composite sector must be a strongly coupled large
N theory in order for the AdS/CFT duality to hold. The two-point function of a
conserved current can be described in such a large N theory by the exchange of
an infinite tower of vector meson states, which carry the quantum numbers of the
corresponding global symmetry, compare (2.42). This is dual to the KK modes of
the respective gauge boson, up to mixing with the elementary gauge boson, which
corresponds to the zero mode. We can resume, that due to the AdS/CFT duality,
there exists a correspondence between
� �
A bulk symmetry G
in the
5D theory
and
� �
A global symmetry G
of the
4D theory
and
�
A tower of composite
�
vector mesons in the adjoint
of G in the 4D theory
.
Therefore, a quark bilinear (by quark we will denote fermions in the elementary sector
in this section),
ψ γµ T a ψ , (3.68)
for an arbitrary element of some Lie algebra T a ∈ g with dimension a , can couple
to a tower of composite mesons if the corresponding group G is a global symmetry of