We explore QCD phase diagram by constructing a holographic QCD model using the Einstein-Maxwell-Scalar system. The chiral transition is investigated by adding a probe scalar and confinement transition is studied by adding a probe string into the system. By interpreting the black hole phase transition in the bulk spacetime as the quarkyonic transition in the dual QCD theory and introducing the bypass mechanism for deconfinement transition, we give an explanation why chiral symmetry breaking and deconfinement transition lines coincide with each other despite their different physical origins.
Within an extended soft wall model, we study the temperature dependence of the lowest vector meson states. Scales are adjusted by using as input the $ρ$ meson mass in vacuum and the velocity of sound from lattice QCD which displays a minimum at $T_{\rm c}$. The melting of the $ρ$ meson occurs at temperatures $\mathcal{O}(T_{\rm c})$.
We discuss the possible validity in QCD of a relation between Green's functions which has been recently suggested by Son and Yamamoto, based on a class of AdS/CFT-inspired models of QCD. Our conclusion is that the relation in question is unlikely to be implemented in QCD.
Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate $ζ$ which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (A…
We discuss classification of defects of various codimensions within a holographic model of pure Yang-Mills theories or gauge theories with fundamental matter. We focus on their role below and above the phase transition point as well as their weights in the partition function. The general result is that objects which are stable and heavy in one phase are becoming very light (tensionless) in the other phase. We argue that the $θ$ dependence of the partition function drastically changes at the phase transition point, and therefore it correlates with stability properties of configurations. Some po…
In this paper we discuss the QCD contribution to the Abelian Debye and magnetic screening masses in a deconfined QCD plasma at finite temperature in the presence of an external magnetic field B. We use a holographic AdS/QCD setup in an AdS Schwarzschield black hole background and show that the electric screening mass has a form similar to the one-loop result in QED. Moreover, we calculate the corrections due to the magnetic field to all orders of B and demonstrate that in the case when magnetic field is large the Debye mass grows linearly with B, while the magnetic screening mass vanishes. The…
Holographic models for the pure gauge QCD vacuum are explored. The holographic renormalization of these models is considered as required by a phenomenological approach that takes the $β$-functions of the models as the only input. This approach is done taking the dilaton as the coordinate orthogonal to the border. This choice greatly simplifies the analysis and gives a geometrical interpretation for the fixed points of the renormalization group flow. Examples are constructed that present asymptotic freedom, confinement of static quarks, either with vanishing or non-vanishing gluon condensate $G…
The eigenvalues of the light-front QCD Hamiltonian, quantized at fixed light-front time τ= t+z/c, predict the hadronic mass spectrum and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. We outline…
Gauge/gravity duality leads to a simple, analytical, and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian. This approach, called "Light-Front Holography", successfully describes the spectroscopy of light-quark meson and baryons, their elastic and transition form factors, and other hadronic properties. The bound-state Schrodinger and Dirac equations of the soft-wall AdS/QCD model predict linear Regge trajectories which have the same slope in orbital angular momentum L and radial quantum number n for both mesons and baryons. Light-front holograp…
We discuss holographic QCD in the Veneziano limit (the V-QCD models), concentrating on phenomena near the "conformal" phase transition taking place at a critical value of the ratio x = N_f/N_c. In particular, we review the results for the S-parameter, the technidilaton, and the masses of the mesons.
The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. In particular, the elastic and transition form factors of the pion and the nucleons are well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra o…
Light-Front Holography is a remarkable consequence of the correspondence between string theory in AdS space and conformal field theories in physical-space time. It allows string modes $Φ(z)$ in the AdS fifth dimension to be precisely mapped to the light-front wavefunctions of hadrons in terms of a specific light-front impact variable $ζ$ which measures the separation of the quark and gluonic constituents within the hadron. This mapping was originally obtained by matching the exact expression for electromagnetic current matrix elements in AdS space with the corresponding exact expression for th…
We reply to L. Ya. Glozman's Comment "Is a consistent holographic description of excited hadrons with fixed $L$ possible?" In general, the solutions of the bound state Hamiltonian equation of motion in QCD have Fock state components with different $L$, and consequently hadronic relativistic wave equations derived in the framework of light-front holography share this property. For example, the proton eigenstate has components with L=0 and L=1. The results of AdS/QCD are consistent with the requirements of chiral symmetry and do not violate any fundamental physical principle. This is further ill…
We consider a holographic study of coupling dependent gravitational waves produced by the cosmic first order QCD phase transition at finite baryochemical potential. In the dual description, the first-order QCD phase transition corresponds to the first-order Hawking-Page phase transition in Gauss-Bonnet gravity. At intermediate coupling, we obtain key quantities characterizing the gravitational wave energy density spectrum. We then find that the gravitational waves might be detected for sufficiently large Gauss-Bonnet coupling, while sound waves play an important role in the spectrum. We also c…
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate $z$ with an invariant light-front coordinate $ζ$ which separates the dynamics of quark and gluon binding from the kinematics of constituent …
It is challenging to quantify chaos of QCD, because non-perturbative QCD accompanies non-local observables. By using holography, we find that QCD strings at large $N_c$ and strong coupling limit exhibit chaos, and measure their Lyapunov exponent at zero temperature. A pair of a quark and an antiquark separated by $L_q$ in the large $N_c$ QCD is dual to a Nambu-Goto string hanging from the spatial boundary of the D4-soliton geometry. We numerically solve the motion of the string after putting a pulse force on its boundaries. The chaos is observed for the amplitude of the force larger than a cer…
We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for a…
We investigate instantons in finite temperature QCD via Witten's holographic QCD. To study the deconfinement phase, we use the setup proposed in [1] (arXiv:1107.4048). We find that the sizes of the instantons are stabilized at certain values both in the confinement and deconfinement phases. This agrees with the numerical result in the lattice gauge theory. Besides we find that the gravity duals of the large and small instantons in the deconfinement phase have different topologies. We also argue that the fluctuation of the topological charges is large in confinement phase while it is exponentia…
One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time, τ= t+z/c -- Dirac's "Front Form". The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically i…
Massive QCD at $θ=π$ breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are su…
The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable $ζ$ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the p…
Finite-density QCD is difficult to study numerically because of the sign problem. We prove that, in a certain region of the phase diagram, the phase quenched approximation is exact to O(Nf/Nc). It is true for any physical observables. We also consider the implications for the lattice simulations and find a quantitative evidence for the validity of the phase quenching from existing lattice QCD results at Nc=3. Our results show that the phase-quench approximation is rather good already at Nc=3, and the 1/Nc correction can be incorporated by the phase reweighting method without suffering from the…
Consistent with cosmological constraints, there are scenarios with the large lepton asymmetry which can lead to the finite baryochemical potential at the cosmic QCD phase transition scale. In this paper, we investigate this possibility in the holographic models. Using the holographic renormalization method, we find the first order Hawking-Page phase transition, between Reissner-Nordstr$\rm\ddot{o}$m AdS black hole and thermal charged AdS space, corresponding to the de/confinement phase transition. We obtain the gravitational wave spectra generated during the evolution of bubbles for a range of…
We perform the first study of baryons in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system in type IIA superstring theory. The baryon is described as a chiral soliton solution in the four-dimensional meson effective action derived from holographic QCD. We also present a brief review of the holographic model from the viewpoints of recent hadron physics and QCD phenomenologies.
Light-Front Holography, a remarkable feature of the AdS/CFT correspondence, maps amplitudes in anti-de Sitter (AdS) space to frame-independent light-front wavefunctions of hadrons in physical space-time. The model leads to an effective confining light-front QCD Hamiltonian and a single-variable light-front Schrodinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is identified with a Lorentz-invariant coordinate zeta which measures the separation of the constituents within a …
Measuring chaos of QCD-like theories is a challenge for formulating a novel characterization of quantum gauge theories. We define a chaos phase diagram of QCD allowing us to locate chaos in the parameter space of energy of homogeneous meson condensates and the QCD parameters such as pion/quark mass. We draw the chaos phase diagrams obtained in two ways: first, by using a linear sigma model, varying parameters of the potential, and second, by using the D4/D6 holographic QCD, varying the number of colors $N_c$ and the 't Hooft coupling constant $λ$. A scaling law drastically simplifies our analy…
The soft-wall AdS/QCD model, modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics. The model predicts a zero-mass pion for zero-mass quarks and a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum $L$ of hadrons and the radial quantum number $N$. Light-Front Holography maps the amplitudes which are functions of the fifth dimension variable $z$ of anti-de Sitter space to a corresponding hadron theory quantized on the light front. The resulting Lorentz-invariant relativistic l…
I survey recent developments in hadron physics which follow from the application of superconformal quantum mechanics and light-front holography. This includes new insights into the physics of color confinement, chiral symmetry, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. I also will discuss some novel features of QCD -- such as color transparency, hidden color, and asymmetric intrinsic heavy-quark phenomena. The elimination of renormalization scale ambiguities and the modification of QCD sum ru…
I review applications of superconformal algebra. light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra. and provide a unified Regge spectroscopy of meson, baryon, and tetraquarks with a universal Regge slope. The pion $q \bar q$ eigenstate is composite but yet has zero mass for $m_q=0.$ Light-Front Holography also pre…
We present in detail the basic ingredients contained in bi-local holography, representing a constructive scheme for reconstructing AdS bulk theories in Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is seen to be given by a double Fourier transform. All order interactions are explicitly specified through the collective action. This generates bulk Feynman (Witten) diagrams (at tree and loop level). We give details of the four-point case evaluation. It is noted that the bi-local construction goes beyond the assumptions in various discussions of non-locality.
QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks in the same 4-plet representation with a universal Regge slope. The pion $q \bar q$ eigenstate has zero mass for $m_q=0.$ The superconformal relations also ca…
A remarkable holographic feature of dynamics in AdS space in five dimensions is that it is dual to Hamiltonian theory in physical space-time, quantized at fixed light-front time τ = t+z/c. This light-front holographic principle provides a precise relation between the bound-state amplitudes in AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The fifth dimension coordinate z is dual to the light front variable ζ describing the invariant separation of the quark constituents. The resulting valence Fock-state wavefuncti…
In heavy-ion collisions, the quark-gluon plasma is produced far from equilibrium. This regime is currently inaccessible by quantum chromodynamics (QCD) computations. We calculate shear transport and entropy far from equilibrium in a holographic model, defining a time-dependent ratio of shear viscosity to entropy density, $η/s$. Large deviations of up to 60% from its near-equilibrium value, $1/4π$, are found for realistic situations at the Large Hadron Collider. We predict the far-from-equilibrium time-dependence of $η/s$ to substantially affect the evolution of the QCD plasma and to impact the…
Light-Front Holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space and frame-independent light-front wavefunctions of hadrons in 3+1 physical space-time, thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD, a useful framework which describes the correspondence between theories in a modified AdS$_5$ background and confining field theories in physical space-time. To a first semiclassical approximation, where quantum loops and quark masses are not included, this approach leads to …
In this thesis, QCD is studied from three different directions, with one overarching theme: holography. The holographic duality allows certain strongly coupled QFTs to be described in terms of much simpler classical gravity in one dimension more. The first direction from which QCD is studied in this thesis is by examining the effects of an external magnetic field on a particular holographic model of QCD, yielding interesting qualitative insight. The second approach examines how, in the same model, one can describe dense baryonic configurations, providing a new way to study the matter composing…
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a nonperturbative effective coupling $α_s^{AdS}(Q^2)$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $ \sim 1$ GeV. The resulting $β$ function appears to capture the essential character…
We study the vacuum structure of three-dimensional $SU(N)$ gauge theory coupled to a Chern-Simons term at level $k$ and to $F$ fundamental Dirac fermions. We use a large $N$ holographic description based on a D3/D7 system in type IIB string theory compactified on a supersymmetry breaking circle. The multiple vacua of the theory and the transitions between them are nicely captured by the dual holographic background. The resulting phase diagram, which we derive both at leading and first subleading orders in the $1/N$ expansion, shows a rich structure where topological field theories, non-linear …
We perform a detailed study of mesonic properties in a class of holographic models of QCD, which is described by the Yang-Mills plus Chern-Simons action. By decomposing the 5 dimensional gauge field into resonances and integrating out the massive ones, we reproduce the Chiral Perturbative Theory Lagrangian up to ${\cal O}(p^6)$ and obtain all the relevant low energy constants (LECs). The numerical predictions of the LECs show minor model dependence, and agree reasonably with the determinations from other approaches. Interestingly, various model-independent relations appear among them. Some of …
Spectra of pions, which are known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking, as well as their relationship with chiral phase transition and pion superfluidity phase transition, have been investigated in the framework of soft-wall AdS/QCD. In chiral limit, it is proved both numerically and analytically that pions are massless Goldstone bosons even at finite temperature, which was usually considered as an assumption in soft-wall models. Above $T_c$, at which chiral condensate $\langle \bar{q}q\rangle$ vanishes, the spectra of pions and scalar mesons merge together, s…
The effect of the complex phase of the fermion determinant is a key question related to the sign problem in finite-density QCD. Recently it has been shown that ignoring the complex phase -- the phase quenching -- does not change physics in a certain region of the phase diagram when a number of colors N_c is large. In this paper we study the effect of the phase quenching within the frameworks of effective models and holographic models. We show, in a unified manner, that the phase quenching gives exact results for any fermionic observables (e.g., chiral condensate) in the mean-field approximatio…
We derive a universal relation for the transverse part of triangle anomalies within a class of theories whose gravity dual is described by the Yang-Mills-Chern-Simons theory. This relation provides a set of sum rules involving the masses, decay constants and couplings between resonances, and leads to the formulas for the matrix elements of the vector and axial currents in the presence of the soft electromagnetic field. We also discuss that this relation is valid in real QCD at least approximately. This may be regarded as the anomaly matching for resonances as an analogue of that for the massle…
Inspired by the model of Jarvinen and Kiritsis, we present a simple holographic model for the on set of chiral symmetry breaking at the edge of the conformal window in QCD in the Veneziano limit. Our most naive model enforces the QCD two loop running coupling on a D3/D7 holographic brane system. The mass of the holographic field, describing the chiral condensate in the model, is driven below the BF bound when the running is sufficiently strong, triggering chiral symmetry breaking for N_f/N_c<2.9. This model though contains too great a remnant of supersymmetry and does not correctly encode the …
We give an overview of recent progress into the infrared structure of QCD based on the gauge/gravity correspondence and light-front quantization, where the color confining interaction for mesons and baryons is determined by an underlying superconformal algebraic structure. This new approach to hadron physics gives remarkable connections and predictions across the entire mass spectrum of hadrons and also describes the infrared behavior of the strong coupling. More recently, an extensive study of form factors, polarized and unpolarized parton distributions and the sea quark contribution to the n…
The purpose of this review is to provide basic ingredients of holographic QCD to non-experts in string theory and to summarize its interesting achievements in nuclear and hadron physics. We focus on results from a less stringy bottom-up approach and review a stringy top-down model with some calculational details.
For (planar) closed self-avoiding loops we construct a "holographic" map from the loop equations of large-N QCD_4 to an effective action defined over infinite rank Hitchin bundles. The effective action is constructed densely embedding Hitchin systems into the functional integral of a partially quenched or twisted Eguchi-Kawai model, by means of the resolution of identity into the gauge orbits of the microcanonical ensemble and by changing variables from the moduli fields of Hitchin systems to the moduli of the corresponding holomorphic de Rham local systems. The key point is that the contour i…
We apply the holographic method to 5D gauge theories on the warped interval. Our treatment includes the scalars associated with the fifth gauge field component, which appear as 4D Goldstone bosons in the holographic effective action. Applications are considered to two classes of models in which these scalars play an important role. In the Composite-Higgs (and/or Gauge-Higgs Unification) scenario, the scalars are interpreted as the Higgs field and we use the holographic recipe to compute its one-loop potential. In AdS/QCD models, the scalars are identified with the mesons and we compute hologra…
Neural Ordinary Differential Equations for Mapping the Magnetic QCD Phase Diagram via Holography
Jilin University（吉林大学）；Ningbo University（宁波大学）；Chinese Academy of Sciences（中国科学院）；Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Chinese Academy of Sciences（中国科学院大学）
We review the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential, comparing the results to those expected at large-$N_c$ QCD, and those in a closely related holographic model. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase, the details of which depend on the model. We argue that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density, which suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large-$…
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the…
The QCD light-front Hamitonian equation derived from quantization at fixed LF time provides a causal, frame-independent, method for computing hadron spectroscopy and dynamical observables. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color confining potential $κ^…
Holography provides a powerful tool to model QCD and other strongly coupled gauge dynamics. As examples of its power to compute in novel environments I review some recent results: these include models of the phase structure of QCD at finite temperature and chemical potential; and computation of time dependent processes at strongly coupled phase transitions.
