We explore the effect of the magnetic field on the QCD phase transition through AdS/CFT correspondence. By introducing an anisotropic magnetic field in the Einstein-Maxwell-Scalar system, a family of analytic solutions is obtained by the potential reconstruction method where the contribution of the magnetic field in the blackening background can be analytically derived. After imposing the kinetic gauge function by requesting the linear Regge spectrum of $J/ψ$ mesons, the contribution of the magnetic field phase diagram can be demonstrated. The results show that the transition temperature will be raising as the magnetic field increases, which is the so-call magnetic catalysis effect. However, if the system is in a strong enough magnetic environment, the transition temperature will be cool down and display the inverse catalysis effect.
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 study the dependence of the chiral condensate on external magnetic field in the context of holographic QCD at large number of flavors. We consider a holographic QCD model where the flavor degrees of freedom fully backreact on the color dynamics. Perturbative QCD calculations have shown that $B$ acts constructively on the chiral condensate, a phenomenon called "magnetic catalysis". In contrast, recent lattice calculations show that, depending on the number of flavors and temperature, the magnetic field may also act destructively, which is called "inverse magnetic catalysis". Here we show tha…
We study the effect of magnetic field $B$ on the critical temperature $T_{c}$ of the confinement-deconfinement phase transition in hard-wall AdS/QCD, and holographic duals of flavored and unflavored $\mathcal{N}=4$ super-Yang Mills theories on $\mathbb{R}^3\times \rm S^1$. For all of the holographic models, we find that $T_{c}(B)$ decreases with increasing magnetic field $B\ll T^2$, consistent with the inverse magnetic catalysis recently observed in lattice QCD for $B\lesssim 1~GeV^2$. We also predict that, for large magnetic field $B\gg T^2$, the critical temperature $T_{c}(B)$, eventually, s…
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…
We investigate the effect of a non-zero magnetic field on the chiral condensate using a holographic QCD approach. We extend the model proposed by Iatrakis, Kiritsis and Paredes in arXiv:1010.1364 that realises chiral symmetry breaking dynamically from 5d tachyon condensation. We calculate the chiral condensate, magnetisation and susceptibilities for the confined and deconfined phases. The model leads, in the probe approximation, to magnetic catalysis of chiral symmetry breaking in both confined and deconfined phases. In the chiral limit, $m_q=0$, we find that in the deconfined phase a sufficie…
Magnetic effects on chiral phase transition have been investigated in a modified soft-wall AdS/QCD model, in which the dilaton field is taken to be negative at the ultraviolet region and positive at the infrared region as in Phys.Rev.D93(2016),101901 and JHEP1604(2016)036. The magnetic field is introduced into the background geometry by solving the Einstein-Maxwell system. After embedding the magnetized background geometry into the modified soft-wall model, the magnetic field dependent behavior of chiral condensate is worked out numerically. It is found that, in the chiral limit, the chiral ph…
In this paper, we study the influence of an external magnetic field in holographic QCD models where the backreaction is modeled in via an appropriate choice of the background metric. We add a phenomenological soft wall dilaton to incorporate better IR behavior (confinement). Elaborating on previous studies conducted by [JHEP 1505 (2015) 121], we first discuss the Hawking-Page transition, the dual of the deconfinement transition, as a function of the magnetic field. We confirm that the critical deconfinement temperature can drop with the magnetic field. Secondly, we study the quark condensate h…
We investigate the phase diagram of QCD-like gauge theories at strong coupling at finite magnetic field $B$, temperature $T$ and baryon chemical potential $μ$ using the improved holographic QCD model including the full backreaction of the quarks in the plasma. In addition to the phase diagram we study the behavior of the quark condensate as a function of $T$, $B$ and $μ$ and discuss the fate of (inverse) magnetic catalysis at finite $μ$. In particular we observe that inverse magnetic catalysis exists only for small values of the baryon chemical potential. The speed of sound in this holographic…
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…
It is well known that very large magnetic fields are generated when the Quark-Gluon Plasma is formed during peripheral heavy-ion collisions. Lattice, holographic, and other studies strongly suggest that these fields may, for observationally relevant field values, induce "inverse magnetic catalysis", signalled by a lowering of the critical temperature for the chiral/deconfinement transition. The theoretical basis of this effect has recently attracted much attention; yet so far these investigations have not included another, equally dramatic consequence of the peripheral collision geometry: the …
We review the holographic approach to electromagnetic phenomena in large N QCD. After a brief discussion of existing holographic models, we concentrate on the improved holographic QCD model extended to include magnetically induced phenomena. We explore the influence of magnetic fields on the QCD ground state, focusing on (inverse) magnetic catalysis of chiral condensate, investigate the phase diagram of the theory as a function of magnetic field, temperature and quark chemical potential, and, finally discuss effects of magnetic fields on the quark-anti-quark potential, shear viscosity, speed o…
We study the chiral symmetry breaking and restoration in $ (2+1) $-dimensional gauge theories from the holographic hard and softwall models. We describe the behavior of the chiral condensate in the presence of an external magnetic field for both models at finite temperature. For the hardwall model we find Magnetic Catalysis (MC) in different set ups. For the softwall model we find Inverse Magnetic Catalysis (IMC) and MC in different situations. We also find for the softwall model a crossover transition from IMC to MC at a pseudocritical magnetic field. This study also shows spontaneous symmetr…
The aim of these lectures is to convey a working knowledge of Light Front Holographic QCD and Supersymmetric Light Front Holographic QCD. We first give an overview of holographic QCD in general and then concentrate on the application of the holographic methods on QCD quantized in the light front form. We show how the implementation of the supersymmetric algebra fixes the interaction and how one can obtain hadron mass spectra with the minimal number of parameters. We also treat propagators and compare the holographic approach with other non-perturbative methods. In the last chapter we describe …
We study the H-dibaryon (uuddss) in holographic QCD for the first time. Holographic QCD is derived from a QCD-equivalent D-brane system ($S^1$-compactified D4/D8/$\overline{\rm D8}$) in the superstring theory via the gauge/gravity correspondence. In holographic QCD, all baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons. In this framework, the H-dibaryon can be described as an SO(3)-type hedgehog state. We present the formalism of the H-dibaryon in holographic QCD, and perform the calculation to investigate its properties in the chiral limit.
We consider a holographic description of the chiral symmetry breaking in an external magnetic field in $ (2+1) $-dimensional gauge theories from the softwall model using an improved dilaton field profile given by $Φ(z) = - kz^2 + (k+k_1)z^2\tanh (k_{2}z^2)$. We find inverse magnetic catalysis for $B<B_c$ and magnetic catalysis for $B>B_c$, where $B_c$ is the pseudocritical magnetic field. The transition between these two regimes is a crossover and occurs at $B=B_c$, which depends on the fermion mass and temperature. We also find spontaneous chiral symmetry breaking (the chiral condensate $σ\no…
We discuss a derivation of the quadratic in fields part of action of bottom-up holographic models from some general properties of the large-Nc limit in QCD.
Recent progress in constructing holographic models for QCD is discussed, concentrating on the bottom-up models which implement holographically the renormalization group flow of QCD. The dynamics of gluons can be modeled by using a string-inspired model termed improved holographic QCD, and flavor can be added by introducing space filling branes in this model. The flavor fully backreacts to the glue in the Veneziano limit, giving rise to a class of models which are called V-QCD. The phase diagrams and spectra of V-QCD are in good agreement with results for QCD obtained by other methods.
Properties of the tensor glueball are discussed in the Witten-Sakai-Sugimoto Model, a top-down holographic approach to the non-perturbative region of Quantum Chromodynamics (QCD).
The H-dibaryon (uuddss) is studied in holographic QCD for the first time. In holographic QCD, four-dimensional QCD, i.e., SU($N_c$) gauge theory with chiral quarks, can be formulated with $S^1$-compactified D4/D8/$\overline{\rm D8}$-brane system. In holographic QCD with large $N_c$, all the baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons, and the H-dibaryon can be described as an SO(3)-type topological soliton with $B=2$. We derive the low-energy effective theory to describe the H-dibaryon in holographic QCD. The H-dibaryon mass is found to be …
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.
Within the bottom-up holographic approach to QCD, the highly excited hadrons are identified with the bulk normal modes in the fifth "holographic" dimension. We show that additional states in the same mass range can appear also from taking into consideration the 5D fields dual to higher dimensional QCD operators. The possible effects of these operators were not taken into account in almost all phenomenological applications. Using the scalar case as the simplest example, we demonstrate that the additional higher dimensional operators lead to a large degeneracy of highly excited states in the Sof…
V-QCD is a class of effective holographic models for QCD which fully includes the backreaction of quarks to gluon dynamics. The physics of the theta-angle and the axial anomaly can be consistently included in these models. We analyze their phase diagrams over ranges of values of the quark mass, N_f/N_c, and theta, computing observables such as the topological susceptibility and the meson masses. At small quark mass, where effective chiral Lagrangians are reliable, they agree with the predictions of V-QCD.
A holographic model of probe quarkonia is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The quarkonia action is modified to account for a systematic study of the heavy-quark mass dependence. We focus on the $J/ψ$ and $Υ$ spectral functions and relate our model to heavy quarkonia formation as a special aspect of hadron phenomenology in heavy-ion collisions at LHC.
We review the recent progress made in using holographic QCD to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models. This requires the summation of an infinite tower of axial vector mesons, which is naturally present in holographic QCD models, and indeed takes care of the longitudinal short-distance constraint due to Melnikov and Vainshtein. Numerically the results of simple hard-w…
A holographic model of probe vector mesons (quarkonia) is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The vector meson action is modified to account for various quark masses. We focus on the $Φ$, $J/ψ$ and $Υ$ meson melting in agreement with hadron phenomenology in heavy-ion collisions at LHC, that is the formation of hadrons at the observed freeze-out temperature of 155 MeV.
Solving the properties of dense QCD matter is an extremely challenging problem because standard theoretical tools do not work at intermediate densities. The gauge/gravity duality may help to provide answers in this region. I give a brief review of recent progress in this field, focusing on the V-QCD model, which is one of the most sophisticated holographic models of QCD. I discuss predictions for the phase diagram, the equation of state, and properties of baryons. I apply these results to analyze the properties of neutron stars and to quark matter production in neutron star mergers.
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.
