Holography, Fractionalization and Magnetic Fields

Four dimensional gravity with a U(1) gauge field, coupled to various fields in asymptotically anti-de Sitter spacetime, provides a rich arena for the holographic study of the strongly coupled (2+1)-dimensional dynamics of finite density matter charged under a global U(1). As a first step in furthering the study of the properties of fractionalized and partially fractionalized degrees of freedom in the strongly coupled theory, we construct electron star solutions at zero temperature in the presence of a background magnetic field. We work in Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source is cloaked by an event horizon. A key ingredient of our solutions is our observation that starting with the standard Landau level structure for the density of states, the electron star limits reduce the charge density and energy density to that of the free fermion result. Using this result we construct three types of solution: One has a star in the infra-red with an electrically neutral horizon, another has a star that begins at an electrically charged event horizon, and another has the star begin a finite distance from an electrically charged horizon.Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly interacting matter in magnetic fields. v2: Updated references and adjusted some phrasing in the introductio

Universal Holographic Chiral Dynamics in an External Magnetic Field

In this work we further extend the investigation of holographic gauge theories in external magnetic fields, continuing earlier work. We study the phenomenon of magnetic catalysis of mass generation in 1+3 and 1+2 dimensions, using D3/D7- and D3/D5-brane systems, respectively. We obtain the low energy effective actions of the corresponding pseudo Goldstone bosons and study their dispersion relations. The D3/D7 system exhibits the usual Gell-Mann--Oakes--Renner (GMOR) relation and a relativistic dispersion relation, while the D3/D5 system exhibits a quadratic non-relativistic dispersion relation and a modified linear GMOR relation. The low energy effective action of the D3/D5 system is related to that describing magnon excitations in a ferromagnet. We also study properties of general Dp/Dq systems in an external magnetic field and verify the universality of the magnetic catalysis of dynamical symmetry breaking.Comment: 41 pages, 11 figures, references adde

Magnon-Like Dispersion Relation from M-Theory

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in $AdS_4\times S^7$ background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin case. In the appendix of the paper, we consider membrane solutions in $AdS_7\times S^4$, which give new relations between the conserved charges.Comment: 16 pages, typos corrected; V3: New section and comments added, to appear in Nucl. Phys.

Operator product expansion of higher rank Wilson loops from D-branes and matrix models

In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.Comment: 28 pages, latex; v2: minor misprints corrected, references adde

Glueballs of Super Yang-Mills from Wrapped Branes

In this paper we study qualitative features of glueballs in N=1 SYM for models of wrapped branes in IIA and IIB backgrounds. The scalar mode, 0++ is found to be a mixture of the dilaton and the internal part of the metric. We carry out the numerical study of the IIB background. The potential found exhibits a mass gap and produces a discrete spectrum without any cut-off. We propose a regularization procedure needed to make these states normalizable.Comment: 22 pages plus a appendixes, 2 figure

Multi-matrix models and emergent geometry

Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or non-emergence of local geometry at strong coupling is captured by observables that effectively measure the mass of off-diagonal excitations about a semiclassical eigenvalue background. We find emergent geometry at strong coupling in models where a mass term regulates an infrared divergence. We also show that our notion of emergent geometry can be usefully applied to fuzzy spheres. Although most of our results are analytic, we have found numerical input valuable in guiding and checking our results.Comment: 1+34 pages, 4 figures. References adde

Non-Abelian (p,q) Strings in the Warped Deformed Conifold

We calculate the tension of $(p,q)$-strings in the warped deformed conifold using the non-Abelian DBI action. In the large flux limit, we find exact agreement with the recent expression obtained by Firouzjahi, Leblond and Henry-Tye up to and including order $1/M^2$ terms if $q$ is also taken to be large. Furthermore using the finite $q$ prescription for the symmetrised trace operation we anticipate the most general expression for the tension valid for any $(p,q)$. We find that even in this instance, corrections to the tension scale as $1/M^2$ which is not consistent with simple Casimir scaling.Comment: 18 pages, Latex, 1 figure; Added a discussion of the case when the warp factor parameter $b\neq 1$ and typos correcte

On the Classical String Solutions and String/Field Theory Duality

We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet time parameter.Comment: LaTeX, 15 pages, no figures; V2: some typos corrected; V3: no corrections, to appear in JHE

Holographic Spectral Functions in Metallic AdS/CFT

We study the holographic D3/D7 setup dual to N=4 supersymmetric Yang-Mills with quenched fundamental matter. We extend the previous analyses of conductivity and photoproduction to the case where there is a finite electric field. Due to the electric field a special region in the D7-brane geometry, labelled the singular shell, appears generically, and the computation of correlators involves a careful study of the indicial exponents both at this singular region and at the horizon. We show that there is a unique choice consistent with the known expression for the electrical conductivity found by Karch and O'Bannon. We explore the parameter space spanned by the quark mass, the baryon density and the electric field. We find a region where the conductivity and photoproduction change rapidly and trace this behavior to competing effects which manifest themselves as a crossover behavior in the probe brane embeddings.Comment: 30 pages, 13 figures, v2. references added, minor corrections mad

Rotating and Orbiting Strings in the Near-Horizon Brane Backgrounds

Using the Schwarzschild-type coordinates in stead of the global ones we reconstruct the classical rotating closed string solutions in the AdS*5 x S*5 backgrounds. They are explicitly described by the Jacobi elliptic and trigonometrical functions of worldsheet coordinates. We study the orbiting closed string configurations in the near-horizon geometries of Dp, NS1 and NS5 branes, and derive the energy and spin of them, whose relation takes a simple form for short strings. Specially in the D5 and NS5 backgrounds we have a linear relation that the energy of the point-like string is proportional to the spin, which is associated with the spectrum of strings in the pp-wave geometries obtained by taking a special Penrose limit on the D5 and NS5 backgrounds.Comment: 15 pages, LaTeX, no figure