Deconfinement and Gluon Plasma Dynamics in Improved Holographic QCD
U. Gursoy, E. Kiritsis, L. Mazzanti, F. Nitti
备注：
LaTeX, 15 pages, 6 eps figures. Added comments and references; corrected misprint in eq. (3.5). A slightly shorter version of this work will appear in Physical Review Letters
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.
We review 5D holographic approaches to finite temperature QCD. Thermodynamic properties of the "hard-wall" and the "soft-wall" models are derived. Various non-realistic features in these models are cured by the set-up of improved holographic QCD, that we review here.
We study the thermodynamics of the hard wall model, which consists in the introduction of an infrared cut-off in asymptotically AdS spaces. This is a toy model for confining backgrounds in the context of the gauge/gravity correspondence. We use holographic renormalization and reproduce the existence of a Hawking Page phase transition recently discussed by Herzog. We also show that the entropy jumps from $N^0$ to $N^2$, which reinforces the interpretation of this transition as the gravity dual of confinement/deconfinement. We also show that similar results hold for the phenomenologically motiva…
The deconfinement phase transition of SU(2) Yang--Mills theory is investigated in the Hamiltonian approach in Coulomb gauge assuming a quasi-particle picture for the grand canonical gluon ensemble. The thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. Above the deconfinement phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved, while the gluon energy, being infrared divergent in the confined phase, becomes infrared finite in the deconfined phase. For the effective gluon mass we…
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…
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
Under a Scherk-Schwarz compactification, the AdS soliton and black brane provide a dual description to a confinement/deconfinement phase transition. We extend this construction to asymptotically Lifshitz spacetimes. In particular, we show that there must be a phase transition between the soliton and black hole if the solutions exist. We also construct these solutions numerically and compute the phase diagram.
The deconfinement phase transition of SU(2) Yang-Mills theory is investigated in the Hamiltonian approach in Coulomb gauge assuming a quasi-particle picture for the grand canonical gluon ensemble. The thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. At the deconfinement phase transition the gluon energy, being infrared divergent in the confined phase, becomes infrared finite in the deconfined phase, while the ghost form factor remains infrared divergent in the deconfined phase but its infrared exponent is approximately halved. Using the l…
We consider a BRST invariant generalization of the "massive background Landau gauge", resembling the original Curci-Ferrari model that saw a revived interest due to its phenomenological success in modeling infrared Yang-Mills dynamics, including that of the phase transition. Unlike the Curci-Ferrari model, however, the mass parameter is no longer a phenomenological input but it enters as a result of dimensional transmutation via a BRST invariant dimension two gluon condensate. The associated renormalization constant is dealt with using Zimmermann's reduction of constants program which fixes th…
We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L x U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4+1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to …
We study the subregion complexity in a semi-analytical holographic QCD model. Two cases with different warped factor are considered and both can realize confinement-deconfinement transition. By studying the behavior of the renormalized holographic complexity density $\hat{\cal C}$ versus the subregion length scale $\ell$, we find that for both cases, $\hat{\cal C}$ always experiences a discontinuity at certain critical value $\ell_c$ in confinement phases, while it is always continuous in deconfinement phases. This property may be seen as a signal to characterize confinement or deconfinement p…
We argue that deconfinement in AdS/QCD models occurs via a first order Hawking-Page type phase transition between a low temperature thermal AdS space and a high temperature black hole. Such a result is consistent with the expected temperature independence, to leading order in 1/N_c, of the meson spectrum and spatial Wilson loops below the deconfinement temperature. As a byproduct, we obtain model dependent deconfinement temperatures T_c in the hard and soft wall models of AdS/QCD. Our result for T_c in the soft wall model is close to a recent lattice prediction.
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 Hawking-Page transition in a holographic model of field theories with momentum dissipation. We find that the deconfinement temperature strictly decreases as momentum dissipation is increased. For sufficiently strong momentum dissipation, the critical temperature goes to zero, indicating a zero-temperature deconfinement transition in the dual field theory.
Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang-Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrare…
We investigate the thermodynamics of the flavour sector of the Sakai-Sugimoto model in the presence of a magnetic field. Renormalizing the euclidean Dirac-Born-Infeld action in the antipodal limit, we find for the confined and deconfined phases positive contributions to the pressures that grow with the magnetic field. We also obtain positive magnetic susceptibilities indicating a paramagnetic behaviour of quarks. Using these results we estimate a λ^2/N_c correction to the deconfinement temperature that decreases as a function of the magnetic field.
Non-central heavy ion collisions lead to the production of a quark gluon plasma with angular momentum. We investigate, using holographic AdS/QCD models, how does rotation of the medium affects the confinement/deconfinement transition temperature $T_c$. In holographic models, this transition is represented by a Hawking-Page process involving two asymptotically anti-de Sitter spaces. The plasma is represented here by extending the holographic approach to anti-de Sitter spaces with cylindrical symmetry. Then, the rotation of the medium is introduced through a Lorentz boost. We consider hard and s…
In the framework of a holographic QCD approach we study an influence of matters on the deconfinement temperature, $T_c$. We first consider quark flavor number ($N_f$) dependence of $T_c$. We observe that $T_c$ decreases with $N_f$, which is consistent with a lattice QCD result. We also delve into how the quark number density $ρ_q$ affects the value of $T_c$. We find that $T_c$ drops with increasing $ρ_q$. In both cases, we confirm that the contributions from quarks are suppressed by $1/N_c$, as it should be, compared to the ones from a gravitational action (pure Yang-Mills).
Gauge theory with light flavor quark is studied by embedding a D7 brane in a deconfinement phase background newly constructed. We find a phase transition by observing a jump of the vacuum expectation value of quark bilinear and also of the derivative of D7 energy at a critical temperature. For the model considered here, we also study quark-antiquark potential to see some possible quark-bound states and other physical quantities in the deconfinement phase.
We study the gravity dual of four dimensional pure Yang-Mills theory through D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it has been widely believed that the confinement phase in the pure Yang-Mills theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase corresponds to the black D4 brane. We inspect this conjecture carefully and show that the correspondence between the black D4 brane and the deconfinement phase is not correct. Instead, by using a slightly different set up, we find an alternative gravity solution called "localized soliton…
Using two different models from holographic quantum chromodynamics (QCD) we study the deconfinement phase transition in $2+1$ dimensions in the presence of a magnetic field. Working in 2+1 dimensions lead us to {\sl exact} solutions on the magnetic field, in contrast with the case of 3+1 dimensions where the solutions on the magnetic field are perturbative. As our main result we predict a critical magnetic field $B_c$ where the deconfinement critical temperature vanishes. For weak fields meaning $B<B_c$ we find that the critical temperature decreases with increasing magnetic field indicating a…
Based on the IR-improved bulk holographic AdS/QCD model which provides a consistent prediction for the mass spectra of resonance scalar, pseudoscalar, vector and axial vector mesons, we investigate its finite temperature behavior. By analyzing the spectral function of mesons and fitting it with a Breit-Wigner form, we perform an analysis for the critical temperature of mesons. The back-reaction effects of bulk vacuum are considered, the thermal mass spectral function of resonance mesons is calculated based on the back-reaction improved action. A reasonable melting temperature is found to be $T…
We present new anisotropic black brane solutions in 5D Einstein-dilaton-two-Maxwell system. The anisotropic background is specified by an arbitrary dynamical exponent $ν$, a nontrivial warp factor, a non-zero dilaton field, a non-zero time component of the first Maxwell field and a non-zero longitudinal magnetic component of the second Maxwell field. The blackening function supports the Van der Waals-like phase transition between small and large black holes for a suitable first Maxwell field charge. The isotropic case corresponding to $ν= 1$ and zero magnetic field reproduces previously known …
We scrutinize various holographic estimations of the deconfinement temperature within the bottom-up AdS/QCD models. A special emphasis is put on the recent idea of isospectral potentials in the holographic approach. It is demonstrated that different models from an isospectral family (i.e., the models leading to identical predictions for the spectrum of hadrons with fixed quantum numbers) result in different predictions for the deconfinement temperature. This difference is found to be quite small in the scalar glueball channel but very large in the vector meson channel which is often used for f…
In the holographic AdS/QCD approach, the confinement/deconfinement transition is associated with the Hawking-Page transition of a thermal anti-de Sitter (AdS) space to an AdS black hole. In the case of the hard wall model, the thermal transition takes place in the planar AdS thanks to the introduction of an infrared cut-off in the geometry. The corresponding thermodynamic entropy of the $SU(N) $ gauge theory jumps from proportional to $N^0$ in the confined hadronic phase to proportional to $N^2$ in the plasma phase, corresponding to the presence of the color degrees of freedom. The Hawking-Pag…
We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon AdS geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the AdS soliton and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have diffe…
We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that holographic CFTs admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the CFT result, and comment on potential extensions to other confining theories.
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.
We discuss the phenomenon of (inverse) magnetic catalysis for both the deconfinement and chiral transition. We discriminate between the hard and soft wall model, which we suitably generalize to include a magnetic field. Our findings show a critical deconfinement temperature going down, in contrast with the chiral restoration temperature growing with increasing magnetic field. This is at odds with contemporary lattice data, so the quest for a holographic QCD model capable of capturing inverse magnetic catalysis in the chiral sector remains open.
We present a simple and intuitive picture for the deconfinement of quarks and gluons at finite temperature: as the temperature increases, QCD behaves like QED at T=0. We show this by calculating the QCD coupling constant as a function of the temperature and of the external momenta used to probe quarks and gluons.
We study confinement-deconfinement phase transition for heavy quarks in a bottom-up holographic QCD model. We consider a black hole background in an Einstein-Maxwell-scalar system and add probe open strings to the background. Combining the various configurations of the open strings and the phase structure of the black hole background itself, we obtain the confinement-deconfinement phase diagram for heavy quarks in the holographic QCD model.
We study confinement-deconfinement phase transition in a holographic soft-wall QCD model. By solving the Einstein-Maxwell-scalar system analytically, we obtain the phase structure of the black hole backgrounds. We then impose probe open strings in such background to investigate the confinement-deconfinement phase transition from different open string configurations under various temperatures and chemical potentials. Furthermore, we study the Wilson loop by calculating the minimal surface of the probing open string world-sheet and obtain the Cornell potential in confinement phase analytically.
We discuss the entropy carried by a quark-antiquark pair, in particular across the deconfinement transition. We therefore rely on a self-consistent solution to Einstein-Maxwell-dilaton gravity, capable of mimicking essential features of QCD. In particular we introduce a novel model that still captures well the QCD confinement and deconfinement phases, while allowing the introduction of a temperature in a phase which resembles the confined phase, this thanks to it being dual to a small black hole. We pay due attention to some subtleties of such model. We confirm the lattice picture of a strong …
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 present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane -- temperature $T$ and chemical potential $μ$. The Cornell potential behavior in this anisotropic mo…
We give an analytical derivation of the confinement/deconfinement phase transition at finite temperature in the $SU(N)$ Yang-Mills theory in the $D$-dimensional space time for $D>2$. For this purpose, we use a novel reformulation of the Yang-Mills theory which allows the gauge-invariant gluonic mass term, and calculate analytically the effective potential of the Polyakov loop average concretely for the $SU(2)$ and $SU(3)$ Yang-Mills theories by including the gauge-invariant dynamical gluonic mass $M$. For $D=4$, we give an estimate on the transition temperature $T_d$ as the ratio $T_d/M$ to th…
The frequency dependent conductivity $σ(ω)$ of the strongly coupled Quark-Gluon Plasma (QGP) is estimated using a bottom up holographic model that can adequately describe recent lattice data for QCD thermodynamics at zero chemical potential. Different choices for the coupling between the bulk gauge field and the other bulk fields that define the background (the metric and a scalar field) are used in order to fit the lattice data for the electric charge susceptibility $χ_2^Q/T^2$. The ratio $σ_{DC}/T$ is found to vary near the deconfinement transition in a way that is similar to recent lattice …
The chiral and deconfinement phase transitions are investigated within the variational Hamiltonian approach to QCD in Coulomb gauge. The temperature $β^{- 1}$ is introduced by compactifying a spatial dimension. Thereby the whole temperature dependence is encoded in the vacuum state on the spatial manifold $\mathbb{R}^2 \times S^1 (β)$. The chiral quark condensate and the dual quark condensate (dressed Polyakov loop) are calculated as function of the temperature. From their inflection points the pseudo-critical temperatures for the chiral and deconfinement crossover transitions are determined. …
Using holographic subregion complexity, we study the confinement-deconfinement phase transition of quantum chromodynamics. In the model we consider here, we observe a connection between the potential energy of probe meson and the behavior of its complexity. Moreover, near the critical point, at which the phase transition takes place, our numerical calculations indicate that we need less information to specify a meson in the non-conformal vacuum than in the conformal one, despite the fact that the non-conformal vacuum has larger energy!
We analyze the holographic entanglement entropy in a soliton background with Wilson lines and derive a relation analogous to the first law of thermodynamics. The confinement/deconfinement phase transition occurs due to the competition of two minimal surfaces. The entropic c function probes the confinement/deconfinement phase transition. It is sensitive to the degrees of freedom (DOF) smaller than the size of a spatial circle. When the Wilson line becomes large, the entropic c function becomes non-monotonic as a function of the size and does not satisfy the usual c-theorem. We analyze the entan…
We evaluate the longitudinal or (chromo-)electric Yang-Mills gluon propagator in the recently proposed center-symmetric Landau gauge at finite temperature [1]. To model the effect of the Gribov copies in the infrared, we use the Curci-Ferrari model which, in turn, allows us to rely on perturbative calculations. At one-loop order in the SU(2) case, the so-obtained longitudinal gluon propagator provides a clear signature for Z2 center-symmetry breaking with a singular behavior, characteristic of a continuous phase transition. This is in sharp contrast with what is found within the standard Landa…
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.
We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its den…
In earlier work, we studied holographic entanglement entropy in QCD phases using a dynamical Einstein-Maxwell-dilaton gravity model whose dual boundary theory mimics essential features of QCD above and below deconfinement. The model although displays subtle differences compared to the standard QCD phases, however, it introduces a notion of temperature in the phase below the deconfinement critical temperature and captures quite well the entanglement and thermodynamic properties of QCD phases. Here we extend our analysis to study the mutual and $n$-partite information by considering $n$ strips w…
We give an analytical derivation of the confinement/deconfinement phase transition at finite temperature in the $SU(N)$ Yang-Mills theory in the $D$-dimensional space time for $D>2$. We elucidate what is the mechanism for quark confinement and deconfinement at finite temperature and why the phase transition occurs at a certain temperature. For this purpose, we use a novel reformulation of the Yang-Mills theory which allows the gauge-invariant gluonic mass term and calculate analytically the effective potential of the Polyakov loop average concretely for the $SU(2)$ and $SU(3)$ Yang-Mills theor…
In this paper the smallest thermal screening mass associated with the correlator of the $CT$-odd operator, $\sim {\rm Tr}F_{μν}\tilde{F}^{μν}$, is determined in strongly coupled non-Abelian gauge plasmas which are holographically dual to non-conformal, bottom-up Einstein+scalar gravity theories. These holographic models are constructed to describe the thermodynamical properties of $SU(N_c)$ plasmas near deconfinement at large $N_c$ and we identify this thermal mass with the Debye screening mass $m_D$. In this class of non-conformal models with a first order deconfinement transition at $T_c$, $…
Recently Herzog has shown that deconfinement of AdS/QCD can be realized, in the hard-wall model where the small radius region is removed in the asymptotically AdS space, via a first order Hawking-Page phase transition between a low temperature phase given by a pure AdS geometry and a high temperature phase given by the AdS black hole in Poincare coordinates. In this paper we first extend Herzog's work to the hard wall AdS/QCD model in curved spaces by studying the thermodynamics of AdS black holes with spherical or negative constant curvature horizon, dual to a non-supersymmetric Yang-Mills th…
We study the deconfinement phase transition in $ (2+1) $-dimensional holographic $ SU(N) $ gauge theories in the presence of an external magnetic field from the holographic hard and soft wall models. We obtain exact solutions for the critical temperature of the deconfinement transition for any range of magnetic field. As a consequence, we find a critical magnetic field $(B_c)$, in which the critical temperature $(T_c)$ vanishes; for $B<B_c$ we have an inverse magnetic catalysis and for $ B>B_c $ we have a magnetic catalysis.
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 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…
We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show the such states make sense from the holographic viewpoint…
In this paper we study the confinement/deconfinement transition in lattice $SU(2)$ QCD at finite quark density and zero temperature. The simulations are performed on an $32^4$ lattice with rooted staggered fermions at a lattice spacing $a = 0.044 \mathrm{~fm}$. This small lattice spacing allowed us to reach very large baryon density (up to quark chemical potential $μ_q > 2000 \mathrm{~MeV}$) avoiding strong lattice artifacts. In the region $μ_q\sim 1000 \mathrm{~MeV}$ we observe for the first time the confinement/deconfinement transition which manifests itself in rising of the Polyakov loop an…
