  The holographic duality between cascading gauge theory and type IIB
supergravity on warped deformed conifold with fluxes reveals exotic thermal
phases with nonzero expectation values of certain operators, persistent to high
temperatures. These phases, in the limit of vanishing the strong coupling scale
of the cascading gauge theory, would realize thermal ordered conformal phases
in relativistic QFTs. We find that the dual Klebanov-Strassler and
Klebanov-Tseytlin black branes in this limit are outside the regime of the
supergravity approximation, rendering the construction of such conformal
ordered states unreliable. While we have been able to construct conformal order
in phenomenologically deformed effective theory of type IIB supergravity
reduced on warped deformed conifold with fluxes, the removal of the deformation
parameter causes the destruction of the thermal conformal ordered phases. Once
again, we find that the holographic models with the conformal ordered phases
are in the String Theory swampland.
