Matrix Models, Geometric Engineering and Elliptic Genera

We compute the prepotential of N=2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kahler and complex moduli of T^2. We use three different methods to obtain this: matrix models, geometric engineering and instanton calculus. Matrix model approach involves summing up planar diagrams of an associated gauge theory on T^2. Geometric engineering involves considering F-theory on elliptic threefolds, and using topological vertex to sum up worldsheet instantons. Instanton calculus involves computation of elliptic genera of instanton moduli spaces on R^4. We study the compactifications of N=2* theory in detail and establish equivalence of all these three approaches in this case. As a byproduct we geometrically engineer theories with massive adjoint fields. As one application, we show that the moduli space of mass deformed M5-branes wrapped on T^2 combines the Kahler and complex moduli of T^2 and the mass parameter into the period matrix of a genus 2 curve.Comment: 90 pages, Late

Adventures in Holographic Dimer Models

We abstract the essential features of holographic dimer models, and develop several new applications of these models. First, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Second, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.Comment: 22 pages, 8 figures; v2: brief description of case of pure D5 lattice added in sec.3; v3: minor typo fixed; v4: minor change

Holographic models for undoped Weyl semimetals

We continue our recently proposed holographic description of single-particle correlation functions for four-dimensional chiral fermions with Lifshitz scaling at zero chemical potential, paying particular attention to the dynamical exponent z = 2. We present new results for the spectral densities and dispersion relations at non-zero momenta and temperature. In contrast to the relativistic case with z = 1, we find the existence of a quantum phase transition from a non-Fermi liquid into a Fermi liquid in which two Fermi surfaces spontaneously form, even at zero chemical potential. Our findings show that the boundary system behaves like an undoped Weyl semimetal.Comment: 64 pages, 19 figure

Large-density field theory, viscosity, and "2kF2k_F" singularities from string duals

We analyze systems where an effective large-N expansion arises naturally in gauge theories without a large number of colors: a sufficiently large charge density alone can produce a perturbative string ('tHooft) expansion. One example is simply the well-known NS5/F1 system dual to $AdS_3\times T^4\times S^3$, here viewed as a 5+1 dimensional theory at finite density. This model is completely stable, and we find that the existing string-theoretic solution of this model yields two interesting results. First, it indicates that the shear viscosity is not corrected by $\alpha'$ effects in this system. For flow perpendicular to the F1 strings the viscosity to entropy ratio take the usual value $1/4\pi$, but for flow parallel to the F1's it vanishes as $T^2$ at low temperature. Secondly, it encodes singularities in correlation functions coming from low-frequency modes at a finite value of the momentum along the $T^4$ directions. This may provide a strong coupling analogue of finite density condensed matter systems for which fermionic constituents of larger operators contribute so-called "$2k_F$" singularities. In the NS5/F1 example, stretched strings on the gravity side play the role of these composite operators. We explore the analogue for our system of the Luttinger relation between charge density and the volume bounded by these singular surfaces. This model provides a clean example where the string-theoretic UV completion of the gravity dual to a finite density field theory plays a significant and calculable role.Comment: 28 pages. v2: added reference

Fermi Surface under Magnetism Instability

In this paper, we study the fermionic excitations near the quantum criticality using gauge/gravity duality. This is motivated by exploring the Fermi surface evolution near the quantum criticality. We construct the gravity dual of "paramagnetic-nematic" phase transition in a continuum limit and study the Fermi surface evolution across this quantum phase transition. We find that there exists non-Fermi liquid with the Fermi surface in the "paramagnetic" phase and the Fermi surface disappears in the "nematic" phase.Comment: 17pages,2 figures, discussions added; terminology correcte

The Spin of Holographic Electrons at Nonzero Density and Temperature

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.Comment: 27 pages, 11 figures; v2: minor changes, published versio

Spatially homogeneous Lifshitz black holes in five dimensional higher derivative gravity

We consider spatially homogeneous Lifshitz black hole solutions in five dimensional higher derivative gravity theories, which can be possible near horizon geometries of some systems that are interesting in the framework of gauge/gravity duality. We show the solutions belonging to the nine Bianchi classes in the pure R^2 gravity. We find that these black holes have zero entropy at non-zero temperatures and this property is the same as the case of BTZ black holes in new massive gravity at the critical point. In the most general quadratic curvature gravity theories, we find new solutions in Bianchi Type I and Type IX cases.Comment: 15 pages, no figure; v2, refs added, version to appear in JHE

Towards a Non-Relativistic Holographic Superfluid

We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we find a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system reenters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.Comment: 13+5 pages, late