Inverse Anisotropic Catalysis in Holographic QCD

We investigate the effects of anisotropy on the chiral condensate in a holographic model of QCD with a fully backreacted quark sector at vanishing chemical potential. The high temperature deconfined phase is a neutral and anisotropic plasma showing different pressure gradients along different spatial directions, similar to the state produced in noncentral heavy-ion collisions. We find that the chiral transition occurs at a lower temperature in the presence of anisotropy. Equivalently, we find that anisotropy acts destructively on the chiral condensate near the transition temperature. These are precisely the same footprints as the "inverse magnetic catalysis" i.e. the destruction of the condensate with increasing magnetic field observed earlier on the lattice, in effective field theory models and in holography. Based on our findings we suggest, in accordance with the conjecture of [1], that the cause for the inverse magnetic catalysis may be the anisotropy caused by the presence of the magnetic field instead of the charge dynamics created by it. We conclude that the weakening of the chiral condensate due to anisotropy is more general than that due to a magnetic field and we coin the former "inverse anisotropic catalysis". Finally, we observe that any amount of anisotropy changes the IR physics substantially: the geometry is $\text{AdS}_4 \times \mathbb{R}$ up to small corrections, confinement is present only up to a certain scale, and the particles acquire finite widths.Comment: 41 pages, 11 figure

On the YM and QCD spectra from five dimensional strings

We consider a non-critical five dimensional string setup which could provide a dual description of QCD in the limit of large number of colors and flavors. The model corresponds to N_c color D3-branes and N_f D4/anti D4-brane pairs supporting flavor degrees of freedom. The matching of the string model spectrum with the dual field theory one is considered. We discuss the consequences of the possible matching of the gravity modes with the light glueballs and the interpretation of the brane spectrum in Yang-Mills and QCD.Comment: 21 pages; V2: added corrections and references to match the published versio

Holography and Thermodynamics of 5D Dilaton-gravity

The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential are analyzed in detail. Such theories are holographically very close to pure Yang-Mills theory in four dimensions. The existence and uniqueness of black-hole solutions is shown. It is also shown that a Hawking-Page transition exists at finite temperature if and only if the potential corresponds to a confining theory. The physics of the transition matches in detail with that of deconfinement of the Yang-Mills theory. The high-temperature phase asymptotes to a free gluon gas at high temperature matching the expected behavior from asymptotic freedom. The thermal gluon condensate is calculated and shown to be crucial for the existence of a non-trivial deconfining transition. The condensate of the topological charge is shown to vanish in the deconfined phase.Comment: LaTeX, 61 pages (main body) + 58 pages (appendix), 25 eps figures. Revised version, published in JHEP. Two equations added in Section 7.4; typos corrected; references adde

Dressed spectral densities for heavy quark diffusion in holographic plasmas

We analyze the large frequency behavior of the spectral densities that govern the generalized Langevin diffusion process for a heavy quark in the context of the gauge/gravity duality. The bare Langevin correlators obtained from the trailing string solution have a singular short-distance behavior. We argue that the proper dressed spectral functions are obtained by subtracting the zero-temperature correlators. The dressed spectral functions have a sufficiently fast fall-off at large frequency so that the Langevin process is well defined and the dispersion relations are satisfied. We identify the cases in which the subtraction does not modify the associated low-frequency transport coefficients. These include conformal theories and the non-conformal, non-confining models. We provide several analytic and numerical examples in conformal and non-conformal holographic backgrounds.Comment: 51 pages, 2 figure

Improved Holographic QCD

We provide a review to holographic models based on Einstein-dilaton gravity with a potential in 5 dimensions. Such theories, for a judicious choice of potential are very close to the physics of large-N YM theory both at zero and finite temperature. The zero temperature glueball spectra as well as their finite temperature thermodynamic functions compare well with lattice data. The model can be used to calculate transport coefficients, like bulk viscosity, the drag force and jet quenching parameters, relevant for the physics of the Quark-Gluon Plasma.Comment: LatEX, 65 pages, 28 figures, 9 Tables. Based on lectures given at several Schools. To appear in the proceedinds of the 5th Aegean School (Milos, Greece

Resolving the M2-brane

We construct deformed, T^2 wrapped, rotating M2-branes on a resolved cone over Q^{1,1,1} and Q^{1,1,1}/Z_2, as well as on a product of two Eguchi-Hanson instantons. All worldvolume directions of these supersymmetric and regular solutions are fibred over the transverse space. These constitute gravity duals of D=3, N=2 gauge theories. In particular, the deformed M2-brane on a resolved cone over Q^{1,1,1} and the S^1 wrapped M2-brane on a resolved cone over Q^{1,1,1}/Z_2 provide explicit realizations of holographic renormalization group flows in M-theory for which both conformal and Lorentz symmetries are broken in the IR region and restored in the UV limit. These solutions can be dualized to supersymmetric type IIB pp-waves, which are rendered non-singular either by additional flux or a twisted time-like direction.Comment: Latex, 23 pages, references adde

A note on the universality of the Hagedorn behavior of pp-wave strings

Following on from recent studies of string theory on a one-parameter family of integrable deformations of $AdS_{5}\times S^{5}$ proposed by Lunin and Maldacena, we carry out a systematic analysis of the high temperature properties of type IIB strings on the associated pp-wave geometries. In particular, through the computation of the thermal partition function and free energy we find that not only does the theory exhibit a Hagedorn transition in both the $(J,0,0)$ and $(J,J,J)$ class of pp-waves, but that the Hagedorn temperature is insensitive to the deformation suggesting an interesting universality in the high temperature behaviour of the pp-wave string theory. We comment also on the implications of this universality on the confinement/deconfinement transition in the dual $\mathcal{N}=1$ Leigh-Strassler deformation of ${\cal N}=4$ Yang-Mills theory.Comment: 25 pages; fixed minor typo; added reference

In search of the QCD-Gravity correspondence

Quantum Chromodynamics (QCD) is the fundamental theory of strong interactions. It describes the behavior of quarks and gluons which are the smallest known constituents of nuclear matter. The difficulties in solving the theory at low energies in the strongly interacting, non-perturbative regime have left unanswered many important questions in QCD, such as the nature of confinement or the mechanism of hadronization. In these lectures oriented towards the students we introduce two classes of dualities that attempt to reproduce many of the features of QCD, while making the treatment at strong coupling more tractable: (1) the AdS/CFT correspondence between a specific class of string theories and a conformal field theory and (2) an effective low-energy theory of QCD dual to classical QCD on a curved conformal gravitational background. The hope is that by applying these dualities to the evaluation of various properties of the strongly-interacting matter produced in heavy ion collisions one can understand how QCD behaves at strong coupling. We give an outline of the applications, with emphasis on two transport coefficients of QCD matter -- shear and bulk viscosities.Comment: 31 pages, 7 figures; Lectures delivered by D. Kharzeev at the International QGP Winter School, Jaipur, India, February 1-3, 200

Supersymmetric defects in the Maldacena-Nunez background

We find supersymmmetric configurations of a D5-brane probe in the Maldacena-Nunez background which are extended along one or two of the spatial directions of the gauge theory. These embeddings are worldvolume solitons which behave as codimension two or one defects in the gauge theory and preserve two of the four supersymmetries of the background.Comment: 37 pages, 2 figures, LaTeX; v2: references adde

Scattering properties of a cut-circle billiard waveguide with two conical leads

We examine a two-dimensional electron waveguide with a cut-circle cavity and conical leads. By considering Wigner delay times and the Landauer-B\"{u}ttiker conductance for this system, we probe the effects of the closed billiard energy spectrum on scattering properties in the limit of weakly coupled leads. We investigate how lead placement and cavity shape affect these conductance and time delay spectra of the waveguide.Comment: 18 pages, 11 figures, accepted for publication in Phys. Rev. E (Jan. 2001