Abstract
AbstractWe construct charged black branes in type IIA flux compactifications that are dual to (2 + 1)-dimensional field theories at finite density. The internal space is a general Calabi-Yau manifold with fluxes, with internal dimensions much smaller than the AdS radius. Gauge fields descend from the 3-form RR potential evaluated on harmonic forms of the Calabi-Yau, and Kaluza-Klein modes decouple. Black branes are described by a four-dimensional effective field theory that includes only a few light fields and is valid over a parametrically large range of scales. This effective theory determines the low energy dynamics, stability and thermodynamic properties. Tools from flux compactifications are also used to construct holographic CFTs with no relevant scalar operators, that can lead to symmetric phases of condensed matter systems stable to very low temperatures. The general formalism is illustrated with simple examples such as toroidal compactifications and manifolds with a single size modulus. We initiate the classification of holographic phases of matter described by flux compactifications, which include generalized Reissner-Nordstrom branes, nonsupersymmetric$ Ad{S_2}\times {{\mathbb{R}}^2} $and hyperscaling violating solutions.
Highlights
A very successful “bottom-up” approach has been to apply AdS/CFT to phenomenological models of Einstein gravity plus matter fields at finite chemical potential
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
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
Summary
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 × Y solutions. The general framework of type IIA flux compactifications on CY manifolds is presented, focusing on the structure and interactions of gauge fields and properties of the field theory duals. Most of this material is review, but applications of CY flux compactifications to holographic systems at finite density have not been considered before, so it is useful to have a self-contained exposition. Our focus here will be on the structures needed for black branes: gauge fields and their interactions, the effective field theory description, and properties of the holographic QFT duals
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