Black Branes in Flux Compactifications Page: 3 of 38
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discovery of new materials, such as high T, superconductors and heavy fermion metals ,
which require going beyond the Fermi liquid paradigm.
A very successful "bottom-up" approach has been to apply AdS/CFT to phenomenolog-
ical models of Einstein gravity plus matter fields at finite chemical potential. Varying the
matter content and interactions has revealed a rich set of phenomena and striking connec-
tions with condensed matter systems. The next step in this program has been to find string
theory realizations of such constructions, and determine which of these phenomena can oc-
cur in a consistent theory of gravity. The best understood microscopic AdS/CFT dual pairs
arise from Freund-Rubin vacua AdSd+2 x Y, with Y a positively curved manifold . These
solutions have the important property that the size of Y is of order of the AdS radius .
The bottom-up models can then be realized as consistent truncations, where solutions of the
(d + 2)-dimensional theory can be lifted to the full supergravity theory, keeping only a finite
number of fields. In this way, it is possible to obtain new supergravity solutions that include
the effects of nonzero chemical potentials or other background fields.
However, the situation is not completely satisfactory, since there is no guarantee that the
solutions generated in this way are minima of the full theory.' Kaluza-Klein (KK) fields not
included in the truncation can develop instabilities, and in general it is extremely hard to
establish the perturbative stability of these solutions. Ultimately, the reason is that there
is no parametric separation between the AdS scale and the internal radius; there is never a
(d+2)-dimensional theory at low energies and KK modes cannot be decoupled. In this work
we will take a different approach: we will construct black branes in string theory which can
be described in terms of a (d + 2)-dimensional effective field theory (EFT), namely a theory
with a small number of fields valid up to a UV cutoff that is parametrically larger than the
masses and AdS scale.
Microscopically, this means that the internal dimensions have to be much smaller than
the AdS radius, so we have a compactification as opposed to a truncation. At the level of
the (d + 2)-dimensional theory, an EFT for black branes is rather different from a consistent
truncation, in that the small number of light fields in the theory determine all the basic low
energy properties, its stability and thermodynamics (at least at the perturbative level). The
price to pay is that in general the higher dimensional solution is known only approximately;
nevertheless, as we explain below, these approximations have negligibly small effects on the
low energy dynamics in perturbatively controlled regimes. In this paper we will accomplish
the above goal by constructing black branes in flux compactifications of string theory. Flux
compactifications  provide tools beyond the Freund-Rubin mechanism which can give rise
to the desired RAds RKK hierarchy. Examples of AdS4 and AdS5 vacua with small
internal dimensions include [7, 8]. We will focus on asymptotically AdS4 solutions, dual to
(2 + 1)-dimensional field theories.
Our investigation is also motivated by constructing models of symmetric phases of mat-
ter that can be stable at very low temperatures. Field theory models of non Fermi liquids
often have relevant operators and suffer from symmetry-breaking instabilities as the tem-
'except in certain special cases where additional symmetries, such as supersymmetry, ensure stability.
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/m1/3/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.