In this dissertation we use the D3/D7 model in gauge/gravity duality to investigate the effects of finite temperature and particle density on matter in strongly coupled super-Yang-Mills gauge theories, which we interpret as models for the quark-gluon plasma (QGP).
We start with an introduction to the AdS/CFT correspondence and the setup we use subsequently. We then investigate the effects of finite temperature and particle density on fundamental matter from three different viewpoints.
(i) We study meson spectra. Our observations at finite temperature and particle density are in qualitative agreement with phenomenological models and experimental observations. They agree with previous publications in the according limits.
(ii) We study the temperature and density dependence of transport properties of fundamental matter in the QGP. In particular, we obtain diffusion coefficients. Furthermore, in a kinetic model we estimate the effects of the coupling strength on meson diffusion and therewith equilibration processes in the QGP.
(iii) We observe the effects of finite temperature and density on the phase structure of fundamental matter in the holographic QGP. We trace out the phase transition lines of different phases in the phase diagram.
The holographic formalism is applied to the calculation of the effective potential for the scalar glueball operator. Three different versions of this operator are defined, and for each we compute the associated effective potential and discuss its properties and scheme ambiguities. Contact is made to earlier attempts to guess this effective potential from the conformal anomaly. We apply our results to the Improved Holographic QCD model calculating the glueball condensate.
We perform the potential analysis in holographic Schwinger effect in a deformed anti-de Sitter (AdS) background with backreaction due to the gluon condensate. We determine the potential by analyzing the classical string action attaching on a probe D3-brane sitting at an intermediate position in the bulk AdS space. It is found that the inclusion of the gluon condensate reduces the production rate, reverse to the effect of the temperature. Also, we evaluate the critical electric field by Dirac-Born-Infeld (DBI) action.
The gluon condensate is very sensitive to the QCD deconfinement transition since its value changes drastically with the deconfinement transition. We calculate the gluon condensate dependence of the heavy quark potential in AdS/CFT to study how the property of the heavy quarkonium is affected by a relic of the deconfinement transition. We observe that the heavy quark potential becomes deeper as the value of the gluon condensate decreases. We interpret this as a dropping of the heavy quarkonium mass just above the deconfinement transition, which is similar to the results obtained from QCD sum ru…
We study phase diagram of the dense holographic gauge matter in the Sakai-Sugimoto model in the presence of the magnetic field above the deconfinement temperature. Even above the deconfinement, quarks could form colour bound states through the remaining strong interaction if the density is large. We demonstrate that in the presence of the magnetic field for a sufficiently large baryon density, the multiquark-pion gradient (MQ-$\mathcal{5}ϕ$) phase is more thermodynamically preferred than the chiral-symmetric quark-gluon plasma. The phase diagrams between the holographic multiquark and the chir…
We study the AC optical and hall conductivities of Dp/Dq-branes intersections in the probe approximation and use sum-rules to study various associated transport coefficients. We determine that the presence of massive fundamental matter, as compared to massless fundamental matter described holographically by a theory with no dimensional defects, reduces the plasma frequency. We further show that this is not the case when the brane intersections include defects. We discuss in detail how to implement correctly the regularization of retarded Green's functions so that the dispersion relations are s…
We study the phase diagram of a holographic QCD using the probe D7 brane in black D3 geometry with finite D-instanton charge. Due to quasi-confining nature of the geometry, baryon vertex can exist outside the horizon so that we can find D7 brane embeddings with finite baryon density and finite chiral condensation as well as an embedding where only quarks are possible but chiral condensation can be zero or non-zero. We study the phase transition and phase diagram between these phases. We also calculated constituent quark mass and binding energy of baryons as fucntion of the density.
The finite temperature physics of the pure glue sector in the improved holographic QCD model of arXiv:0707.1324 and arXiv:0707.1349 is addressed. The thermodynamics of 5D dilaton gravity duals to confining gauge theories is analyzed. We show that they exhibit a first order Hawking-Page type phase transition. In the explicit background of arXiv:0707.1349, we find T_c = 235 MeV. The temperature dependence of various thermodynamic quantities such as the pressure, entropy and speed of sound is calculated. The results show a good agreement with the corresponding lattice data.
Gauge theory/string theory holographic correspondence for ${\cal N}=4$ supersymmetric Yang-Mills theory is well under control in the planar limit, and for large (infinitely large) 't Hooft coupling, $λ\to \infty$. Certain aspects of the correspondence can be extended including ${\cal O}(λ^{-3/2})$ corrections. There are no reliable first principle computations of the ${\cal N}=4$ plasma non-equilibrium properties beyond the stated order. We show extreme sensitivity of the non-hydrodynamic spectra of holographic ${\cal N}=4$ SYM plasma to ${\cal O}(λ^{-3})$ corrections, challenging any conclusi…
A heavy quark moving through a strongly coupled deconfined plasma has a holographic dual description as a string moving in a black brane geometry. We apply the holographic Wilsonian renormalization method to derive a holographic effective string action dual to the heavy quark. The effective action only depends on the geometry between the black brane horizon and a cutoff localized in the radial direction, corresponding to the IR of the dual theory. We derive RG flow equations for the coefficients in the effective action and show that the force acting on the heavy quark is independent of the pos…
Prior attempts to construct the gravity dual of boost-invariant flow of N=4 supersymmetric Yang-Mills gauge theory plasma suffered from apparent curvature singularities in the late time expansion. This Letter shows how these problems can be resolved by a different choice of expansion parameter. The calculations presented correctly reproduce the plasma energy-momentum tensor within the framework of second order viscous hydrodynamics.
A novel technique is used to compute the bulk viscosity of high temperature holographic gauge theory plasmas with softly broken conformal symmetry. Working in a black hole background which corresponds to a non-trivial solution to the Navier-Stokes equation, and using a Ward identity for the trace of the stress-energy tensor, it is possible to obtain an analytic expression for the bulk viscosity. This can be used to verify the high temperature limit of a conjectured bound on the bulk viscosity for these theories. The bound is saturated when the conformal symmetry-breaking operator becomes margi…
We review construction of the improved holographic models for QCD-like confining gauge theories and their applications to the physics of the Quark-gluon plasma. We also review recent progress in this area of research. The lecture notes start from the vacuum structure of these theories, then develop thermodynamic and hydrodynamic observables and end with more advanced topics such as the holographic QCD in the presence of external magnetic fields. This is a summary of the lectures presented at the 56th Cracow School of Theoretical Physics in Spring 2016 at Zakopane, Poland.
The phase diagram of quark gluon plasma (QGP) formed at a very early stage just after the heavy ion collision is obtained by using a holographic dual model for the heavy ion collision. In this dual model colliding ions are described by the charged shock gravitational waves. Points on the phase diagram correspond to the QGP or hadronic matter with given temperatures and chemical potentials. The phase of QGP in dual terms is related to the case when the collision of shock waves leads to formation of trapped surface. Hadronic matter and other confined states correspond to the absence of trapped s…
The aim of this work is to study the holographic dual to the gauge theory with a nonzero gluon condensate. We check for consistency the holographic way of describing the condensate and calculate the expectation value of a small Wilson loop in the presence of the gluon condensate, thus obtaining the relevant coefficient in the operator product expansion of the small loop in different holographic models. We also study the effect of the condensate on the Gross-Ooguri phase transition in the correlator of two circular Wilson loops in parallel and concentric configurations. In the numerical study o…
I discuss the possibility that the quark-gluon plasma at strong coupling admits a description in terms of a black hole in asymptotically anti-de Sitter space.
We derive a holographic prediction of the deconfinement temperature $T_c$ at vanishing chemical potential within a simplest AdS/QCD model with dynamical dilaton. Our analysis leads to a linear relation between $T_c^4$ and the gluon condensate. After normalizing this relation to the lattice data for $SU(3)$ pure gauge theory, the standard phenomenological value of gluon condensate from QCD sum rules leads to the prediction $T_c=156$ MeV which is in a perfect agreement with the modern lattice results and freeze-out temperature measured by the ALICE Collaboration.
We study the thermodynamics and the jet quenching parameter of a black hole solution dual to a SQCD-like plasma which includes the backreaction of fundamental flavors. The free energy is calculated in several ways, including some recently proposed holographic renormalization prescriptions. The validity of the latter is confirmed by the consistency with the other methods. The resulting thermodynamic properties are similar to the Little String Theory ones: the temperature is fixed at the Hagedorn value and the free energy is vanishing. Finally, an accurate analysis of the relevant string configu…
We construct a gravity dual of a boost-invariant flow of an N=4 SU(N) supersymmetric Yang-Mills gauge theory plasma with chemical potential. We present both a first-order corrected late-time solution in Eddington-Finkelstein coordinates and a zeroth-order solution in parametric form in Fefferman-Graham coordinates. The resulting background takes the form of a time-dependent AdS Reissner-Nordstroem-type black hole whose horizons move into the bulk of the AdS space. The solution correctly reproduces the energy and charge density as well as the viscosity of the plasma previously computed in the l…
In this work, we perform a holographic analysis to study non local observables associated to a uniformly \textit{boosted} strongly coupled large $N$ thermal plasma in $d$-dimensions. In order to accomplish the holographic analysis, the appropriate dual bulk theory turns out to be $d+1$ dimensional \textit{boosted} AdS-Schwarzschild blackhole background. In particular, we compute entanglement entropy of the boosted plasma at high temperature living inside a strip geometry with entangling width $l$ in the boundary at a particular instant of time. We also study the two-point correlators in the bo…
We obtain the gluon parton distribution functions (PDFs) in the proton within the extended light-front holographic QCD framework, where the proton couples with the spin-two Pomeron in Anti-de Sitter space, together with constraints imposed by the Veneziano model. The gluon helicity asymmetry, after satisfying the perturbative QCD constraints at small and large longitudinal momentum regions, agrees with existing experimental measurements. The polarized gluon distribution is consistent with global analyses. We predict the gluon helicity contribution to the proton spin, $ΔG=0.221^{+0.056}_{-0.044…
We use the holographic principle to study quark jets with trailing strings in an expanding plasma that asymptotes Bjorken hydrodynamics. We make use of the fact that the trailing string is the locus of the light delay in bulk to obtain the explicit form for quark jets in the expanding plasma. From the trailing string solution we calculate the drag coefficient of a heavy quark in the strongly coupled expanding plasma. The energy scaling of the maximum penetration length of an ultrarelativistic light quark jet using light rays in bulk is estimated.
Holography provides a novel method to study the physics of Quark Gluon Plasmas, complementary to the ordinary field theory and lattice approaches. In this context, we analyze the informations that can be obtained for strongly coupled Plasmas containing dynamical flavors, also in the presence of a finite baryon chemical potential. In particular, we discuss the jet quenching and the hydrodynamic transport coefficients.
We propose a general method for finding a string-like meson spectrum which is based on a certain condition for the breaking of closed gluon string. A model is constructed that successfully realizes the proposed method. The model is based on the holographic Soft Wall model for QCD and the use of the Wilson confinement criterion. We applied our approach to the vector and scalar cases and obtained numerical predictions for the intercepts of corresponding Regge like radial meson spectra. A good agreement is obtained both with the existing experimental data and with some other known phenomenologica…
We estimate the ratio of the thermalization time over the freeze-out time using a holographic AdS-Vaidya model for quark-gluon plasma formed in the heavy ion collisions. In the model the process of thermalization is described as formation of the black hole in AdS space while dethermalization process, related with the freeze-out, as the black hole evaporation due to the Hawking radiation that is modeled by the Vaidya metric with a negative mass. In this model the thermalization takes place only at small scales and absent in the infrared region. At small scales the system tends towards a state o…
We study the velocity statistics distribution of an external heavy particle in holographic fluids. We argue that when the dual supergravity background has a finite temperature horizon the velocity statistics goes generically as $1/v$, compatible with the jet-quenching intuition from the quark-gluon plasma. A careful analysis of the behavior of the classical string whose apparent worldsheet horizon deviates from the background horizon reveals that other regimes are possible. We numerically discuss two cases: the magnetized quark-gluon plasma and a model of superfluid flow. We explore a range of…
Using the framework of higher-form global symmetries, we examine the regime of validity of force-free electrodynamics by evaluating the lifetime of the electric field operator, which is non-conserved due to screening effects. We focus on a holographic model which has the same global symmetry as that of low energy plasma and obtain the lifetime of (non-conserved) electric flux in a strong magnetic field regime. The lifetime is inversely correlated to the magnetic field strength and thus suppressed in the strong field regime.
We consider a black hole solution with a non-trivial dilaton from IIB super gravity which is expected to describe a strongly coupled hot gauge plasma with non-vanishing gluon condensation present. We construct a rotating and moving baryon to probe the screening and phases of the plasma. Melting of the baryons in hot plasma in this background had been studied previously, however, we show that baryons melt much lower temperature than has been suggested previously.
In this study, the gauge/string duality is used to investigate the dynamics of a moving heavy quark in a strongly coupled, non-conformal plasma. The drag force in this non-conformal model is smaller than that of $\mathcal{N} = 4$ supersymmetric Yang-Mills (SYM) plasma and decreases as the level of non-conformality is increased. At intermediate temperatures, the world-sheet temperature, which is derived numerically by calculating the world-sheet horizon, deviates from its conformal value, but at high temperatures, it tends to its conformal value.
We study Brownian motion of a heavy quark in field theory plasma in the AdS/CFT setup and discuss the time scales characterizing the interaction between the Brownian particle and plasma constituents. In particular, the mean-free-path time is related to the connected 4-point function of the random force felt by the Brownian particle. By holographically computing the 4-point function and regularizing the IR divergence appearing in the computation, we write down a general formula for the mean-free-path time, and apply it to the STU black hole which corresponds to plasma charged under three U(1) R…
We present the results of a holographic model for heavy vector mesons inside a plasma at finite temperature and density. The spectral function shows a nice description of the dissociation of the mesons in the medium, corresponding to the decrease in the height of the peaks as the temperature and (or) the density increase. We consider the case of bottomonium states at finite temperature and also the case of charmonium dissociation at zero temperature but finite chemical potential.
We review the construction of gravitational solutions holographically dual to N=1 quiver gauge theories with dynamical flavor multiplets. We focus on the D3-D7 construction and consider the finite temperature, finite quark chemical potential case where there is a charged black hole in the dual solution. Discussed physical outputs of the model include its thermodynamics (with susceptibilities) and general hydrodynamic properties.
We study in detail the transverse collective modes of simple holographic models in presence of electromagnetic Coulomb interactions. We render the Maxwell gauge field dynamical via mixed boundary conditions, corresponding to a double trace deformation in the boundary field theory. We consider three different situations: (i) a holographic plasma with conserved momentum, (ii) a holographic (dirty) plasma with finite momentum relaxation and (iii) a holographic viscoelastic plasma with propagating transverse phonons. We observe two interesting new features induced by the Coulomb interactions: a mo…
The density of states and energy spectrum of the gluon radiation are calculated for the color current of an expanding hydrodynamic skyrmion in the quark gluon plasma with a semiclassical method. Results are compared with those in literatures.
We provide a short review of the hydrodynamical properties of a class of strongly coupled thermal gauge theories, coupled to massless fundamental flavor fields, having a dual supergravity description. The analysis is valid for more general classes of nearly conformal holographic plasmas, where the breaking of conformality is driven by marginally (ir)relevant deformations.
We analyse mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic consideration imply that large-spin meso…
We analytically compute the out-of-equilibrium direct photon production rate and electric conductivity, in a strongly coupled and expanding Bjorken plasma, from holography. Our results are valid at late times where the expanding plasma asymptotes Bjorken hydrodynamics. The out-of-equilibrium rates are substantially harder and larger, early on in the Bjorken expansion phase.
We present a holographic analysis of diffractive photoproducton of charmonium $J/ψ$ and upsilonium $Υ$ on a proton, considered as a bulk Dirac fermion, for all ranges of $\sqrt{s}$, i.e., from near threshold to very high energy. Using the bulk wave functions of the proton and vector mesons, within holographic QCD, and employing Witten diagrams in the bulk, we compute the diffractive photoproduction amplitude of $J/ψ$ and $Υ$. The holographic amplitude shows elements of the strictures of vector meson dominance (VMD). It is dominated by the exchange of a massive graviton or $2^{++}$ glueball res…
We employ methods of gauge/string duality to analyze the Brownian motion and the concomitant Langevin equation of a heavy quark in a strongly coupled, thermal, anisotropic Yang-Mills plasma. We consider fluctuations both along and perpendicular to the direction of anisotropy and study the effects of anisotropy on the drag coefficient, the diffusion constant and the Langevin coefficient for both the directions. We also verify the fluctuation-dissipation theorem for Brownian motion in an anisotropic medium.
We present a string theory construction of a gravity dual of a spatially modulated phase. In our earlier work, we showed that the Chern-Simons term in the 5-dimensional Maxwell theory destabilizes the Reissner-Nordstrom black holes in anti-de Sitter space if the Chern-Simons coupling is sufficiently high. In this paper, we show that a similar instability is realized on the worldvolume of 8-branes in the Sakai-Sugimoto model in the quark-gluon plasma phase. We also construct and analyze a non-linear solution describing the end-point of the transition. Our result suggests a new spatially modulat…
The generating functional for hard thermal loops in QCD is rewritten in terms of a gauged WZNW action by introducing an auxiliary field. This shows in a simple way that the contribution of hard thermal loops to the energy of the quark-gluon plasma is positive.
Starting from the kinetic formulation of the hard thermal loop effective theory, we have (re)derived the collision terms for soft modes of order $g^2 T \log(1/g)$ by averaging the statistical fluctuations in the plasma.
In this work I explore theoretical and phenomenological implications of chemical potentials and charge densities inside a strongly coupled thermal plasma, using the gauge/gravity correspondence. Strong coupling effects discovered in this model theory are interpreted geometrically and may be taken as qualitative predictions for heavy ion collisions at RHIC and LHC. In particular I examine the thermodynamics, spectral functions, transport coefficients and the phase diagram of the strongly coupled plasma. For example stable mesons, which are the analogs of the QCD Rho-mesons, are found to survive…
Initially produced quark-gluon matter at RHIC and LHC does not have a temperature. A quark-gluon plasma has a high temperature. From this quark-gluon matter to the quark-gluon plasma is the early thermalization or the rapid creation of temperature. Elastic three-parton scattering plays a key role in the process. The temperature originates from the two-parton scattering, the three-parton scattering, the four-parton scattering and so forth in quark-gluon matter.
Considering the classical two-point correlators built from (axial)-vector, scalar \bar qq and gluonium currents, we confront results obtained using the SVZ + 1/q^2 expansion to the ones from some QCD holographic models in the Euclidian region and with negative dilaton Φ_i(z)=- |c_i^2| z^2. We conclude that the presence of the 1/q^2-term in the SVZ-expansion due to a tachyonic gluon mass appears naturally in the Minimum Soft Wall (MSW) and the Gauge/String Dual (GSD) models which can also reproduce semi-quantitatively some of the higher dimension condensate contributions appearing in the OPE. T…
Peripheral collisions of heavy ions can give rise to extremely intense magnetic fields. It has been suggested that these fields might invalidate the holographic description of the corresponding quark-gluon plasmas, assuming that these can be modelled by strongly coupled field theories. In the case of the plasmas produced in collisions at the RHIC facility (including in the beam energy scans), it is known how to deal with this problem: one has to take into account the large angular momenta generated in these plasmas, and the effects of the baryonic chemical potential. But this does not work for…
Based on a holographic far-from-equilibrium calculation of the chiral magnetic effect~(CME) in an expanding quark gluon plasma, we study collisions at various energies. We compute the time evolution of the CME current in the presence of a time-dependent axial charge density and subject to a time-dependent magnetic field. The plasma expansion leads to a dilution of the CME current. We study distinct combinations of how the initial magnetic field and initial axial charge behave with changing initial energy as proposed in previous literature. Most scenarios we consider lead to an increasing time-…
We study the conductivity and shear viscosity tensors of a strongly coupled N=4 super-Yang-Mills plasma which is kept anisotropic by a theta parameter that depends linearly on one of the spatial dimensions. Its holographic dual is given by an anisotropic axion-dilaton-gravity background and has recently been proposed by Mateos and Trancanelli as a model for the pre-equilibrium stage of quark-gluon plasma in heavy-ion collisions. By applying the membrane paradigm which we also check by numerical evaluation of Kubo formula and lowest lying quasinormal modes, we find that the shear viscosity pure…
We study far-from-equilibrium physics of strongly interacting plasmas at criticality and zero charge density for a wide range of dynamical scaling exponents z in d dimensions using holographic methods. In particular, we consider homogeneous isotropization of asymptotically Lifshitz black branes with full backreaction. We find stable evolution and equilibration times that exhibit small dependence of z and are of the order of the inverse temperature. Performing a quasinormal mode analysis we find a corresponding narrow range of relaxation times, fully characterized by the fraction z/(d-1). For z…
We present new results on the decay patterns of scalar and tensor glueballs in the top-down holographic Witten-Sakai-Sugimoto model. This model, which has only one free dimensionless parameter, gives semi-quantitative predictions for the vector meson spectrum, their decay widths, and also a gluon condensate in agreement with SVZ sum rules. The holographic predictions for scalar glueball decay rates are compared with experimental data for the widely discussed gluon candidates f0(1500) and f0(1710).
