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perature is lowered. Similar issues are encountered in the gravity side, for instance with
superconducting  or translation-breaking  instabilities. While these instabilities can
lead to interesting broken phases, it is important to develop tools to stabilize symmetric
phases by lifting the dangerous relevant operators. For this, we need to find gravity solu-
tions where all the scalar fields have positive masses. Fortunately, during the last decade
there has been important progress in developing mechanisms to lift all the light moduli in
string compactifications. The motivation has been to construct string vacua that could give
realistic models of cosmology or particle physics, and we will apply these results to stabilize
phases of condensed matter systems. Combining fluxes and certain orbifold operations we
will exhibit simple flux compactifications that describe holographic QFTs where the only
relevant operator is the global current that gives rise to the chemical potential, and all scalar
operators are irrelevant. Furthermore, the operators that are charged under the chemical po-
tential -the strongly coupled "electrons"- have parametrically large dimensions. This class
of theories is then an ideal laboratory for studying interesting IR symmetric phases.
1.1 Basic setup and structure of the paper
Before beginning our analysis, let us describe the basic setup. We are mainly interested
in (2 + 1)-dimensional QFTs at finite density, so we will focus on flux compactifications
that admit AdS4 x Y solutions. The internal manifold Y is taken to be a six-dimensional
Calabi-Yau (CY) manifold. The main motivation for this is that the low energy theory for
CY compactifications is very well understood . Moreover, in the perturbative regime of
weak string coupling and large volume, the low energy theory depends only on topological
information of the manifold, such as dimensions of cycles and cohomology. The EFT for
black branes will then apply very generally to all CYs, making it a powerful and simple tool
to analyze the low energy physics.
Now we need to explain how the main ingredients required for black brane solutions -a
negative cosmological constant and gauge fields- are obtained in this setup. The internal
space is Ricci-flat, so there is no negative contribution to the potential energy from the
internal curvature (unlike the case of Freund-Rubin vacua). The negative energy will come
from orientifold planes, and balancing their contribution against fluxes (from color branes)
can produce AdS vacua. With the goal of stabilizing all the light scalars, we will work
with type HA string theory, where AdS solutions with the desired properties are already
Models based on consistent truncations typically have gauge fields from the isometrics of
the positively curved internal space Y. However, CY manifolds have no isometrics, so we need
to look for other sources of gauge fields. Already in the early works on CY compactifications
it was noticed that evaluating the RR potentials on the nontrivial cohomology forms can
give rise to gauge fields; see  for a review and references. Decomposing the type HA
2Stabilizing all moduli in type IIB CY compactifications requires nonperturbative effects . It would
be interesting to understand these instanton effects in the dual QFT.
Published in arXiv:1306.3982.
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Torroba, Gonzalo & Wang, Huajia. Black Branes in Flux Compactifications, article, August 15, 2013; United States. (digital.library.unt.edu/ark:/67531/metadc834243/m1/4/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.