Holographic QCD Model Research Articles

Holographic approach to the light-by-light contribution to the muon (g-2)

We discuss how holographic models of QCD are used to study the the hadronic light-by-light (HLbL) scattering amplitude contribution to the muon anomalous magnetic moment. After a brief description of the various models, we focus on a particular one, introduced by Hirn and Sanz, emphasizing the role it assigns to the pion, and the vector and-axial vector resonances. We review how the parameters of the model are fixed by imposing condition on the low energy and the deep Euclidean limit of two-point correlators of QCD vector and axial vector currents. We then focus on the evaluation of the three-point axial-vector-vector current correlator and the pion anomalous transition form factor to be used in the one-pion exchange HLbL diagram and study its asymptotic properties. Finally, we present preliminary results on the four vector current correlator that defines the Hadronic Light-by-Light tensor. We find that axial-vector resonances play an important rule in recovering the correct asymptotic behaviour predicted by QCD at large Euclidean momenta.

Non-derivative axionic couplings to nucleons at large and small N

Among the possible CP-odd couplings of the axion to ordinary matter, the most relevant ones for phenomenology are the Yukawa couplings to nucleons. We analyze such non-derivative couplings within three different approaches: standard effective field theory, the Skyrme model and holographic QCD. In all the cases, the couplings can be related to the CP-odd non-derivative couplings to nucleons of the low-lying mesons and the η′. Using the effective field theory approach we discuss how to derive the expressions for the CP-odd interaction terms as functions of the parameters of the effective Lagrangian at generic number of colors Nc and flavors Nf. Then, we compute the CP-odd couplings to nucleons of the axion, the η′ and the pseudo-Goldstone mesons in both the Skyrme and the holographic QCD model with Nf = 2, 3. We present model-independent expressions for the coefficients of the non-derivative axion-nucleon couplings. This allows us to provide quantitative estimates of these couplings.

Thermodynamics of AdS5 black holes: holographic QCD and Stückelberg model

We explore the thermodynamics of AdS5 black holes in two models: i) an improved holographic QCD model with a simple dilaton potential, and ii) the Stückelberg model in 5D. In the former case, by applying techniques of singular perturbation theory, we obtain a resummation of the naive expansion at high temperatures, providing a good fit to the lattice data for the trace anomaly. In the latter, we find a solution of the equations of motion by considering an expansion in the conformal dimension of the current associated to the gauge field.

Pseudoscalar transition form factors and the hadronic light-by-light contribution to the anomalous magnetic moment of the muon from holographic QCD

We revisit the predictions for the pseudoscalar-photon transition form factors in bottom-up and top-down holographic QCD models which only use the pion decay constant and the $\rho$ meson mass as input. We find remarkable agreement with the available experimental data for the single-virtual $\pi^0$ form factor that have recently been extended to lower momenta by BESIII, down to 0.3 GeV$^2$. The bottom-up models moreover turn out to be roughly consistent with recent experimental results obtained by BaBar for the double-virtual $\eta'$ form factor at large momenta as well as with a recent lattice extrapolation for the double-virtual $\pi^0$ form factor. Calculating the pion pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon, we find that the bottom-up models in question span the range $a_\mu^{\pi^0}=6.1(4)\cdot 10^{-10}, which is somewhat lower than estimated previously by approximating these holographic predictions through simple interpolators, and in remarkably good agreement with recent results based on a dispersive approach or lattice simulations.

Conformal symmetry breaking in holographic QCD

In this paper, we investigate a simple holographic model which describes the conformal symmetry breaking at zero temperature. The model is implemented in the context of effective holographic models for QCD described by the Einstein-dilaton equations. The realization of spontaneous conformal symmetry breaking shows a massless state in the spectrum. The existence of this state is confirmed when we compute the two-point correlation function of the scalar operator in the dual field theory, where it has a pole. On the other hand, when there is an explicit conformal symmetry breaking the massless state becomes massive, which in the dual gravitational theory is related to a deformation of the Anti-de Sitter (AdS) background by a massive scalar (dilaton) field. Moreover, we show the mass dependence on the conformal dimension of the lightest state.

Drag force on heavy quarks from holographic QCD * * Supported by Guizhou Provincial Key Laboratory Of Computational Nano-Material Science (2018LCNS002)

We study the drag force of a relativistic heavy quark using a holographic QCD model with conformal invariance broken by a background dilaton. The effects of the chemical potential and the confining scale on this quantity are analyzed. The drag force in this model is shown to be larger than that of supersymmetric Yang-Mills (SYM) plasma. In particular, the inclusion of the chemical potential and confining scale both enhance the drag force, in agreement with earlier findings. Moreover, we discuss how the chemical potential and confining scale influence the diffusion coefficient.

Elastic proton-proton scattering at LHC energies in holographic QCD

The cross sections of the high energy proton-proton scattering are studied in a holographic QCD model, focusing on the Regge regime. In our model setup, the involved nonperturbative partonic dynamics is described by the Pomeron exchange, which is realized by applying the Reggeized spin-2 particle propagator together with the proton gravitational form factor obtained from the bottom-up AdS/QCD model. Our model includes three adjustable parameters which are to be fitted by experimental data. We show that both the resulting differential and total cross sections are consistent with data, including the ones recently measured at sqrt{s} = 13 TeV by the TOTEM collaboration at the LHC. Our results imply that the present framework works well in the considered TeV scale, and further applications to other high energy scattering processes, in which the involved strong interaction can be approximated by the Pomeron exchange, are possible.

Kaon form factor in holographic QCD

The kaon form factor in the spacelike region is calculated using a holographic QCD model with the "bottom-up" approach. We found that our result for the kaon form factor in low $Q^2$ has a remarkable agreement with the existing data, where $Q^2$ is the four-momentum transfer squared. The charge radius of the kaon, as well as the kaon decay constant, are found to be in a good agreement with the experiment data. We then predict the kaon form factor in the asymptotic region (larger $Q^2$) showing $1/Q^2$ behavior, which is consistent with the perturbative QCD prediction.

Melting of scalar mesons and black-hole quasinormal modes in a holographic QCD model

A holographic model for QCD is employed to investigate the effects of the gluon condensate on the spectrum and melting of scalar mesons. We find the evolution of the free energy density with the temperature, and the result shows that the temperature of the confinement/deconinement transition is sensitive to the gluon-condensate parameter. The spectral functions (SPFs) are also obtained and show a series of peaks in the low-temperature regime, indicating the presence of quasiparticle states associated to the mesons, while the number of peaks decreases with the increment of the temperature, characterizing the quasiparticle melting. In the dual gravitational description, the scalar mesons are identified with the black-hole quasinormal modes (QNMs). We obtain the spectrum of QNMs and the dispersion relations corresponding to the scalar-field perturbations of the gravitational background, and find their dependence with the gluon-condensate parameter.

Inverse anisotropic catalysis in holographic QCD

We investigate the effects of anisotropy on the chiral condensate in a holographic model of QCD with a fully backreacted quark sector at vanishing chemical potential. The high temperature deconfined phase is therefore a neutral and anisotropic plasma showing different pressure gradients along different spatial directions, similar to the state produced in noncentral heavy-ion collisions. We find that the chiral transition occurs at a lower temperature in the presence of anisotropy. Equivalently, we find that anisotropy acts destructively on the chiral condensate near the transition temperature. These are precisely the same footprints as the “inverse magnetic catalysis” i.e. the destruction of the condensate with increasing magnetic field observed earlier on the lattice, in effective field theory models and in holography. Based on our findings we suggest, in accordance with the conjecture of [1], that the cause for the inverse magnetic catalysis may be the anisotropy caused by the presence of the magnetic field instead of the charge dynamics created by it. We conclude that the weakening of the chiral condensate due to anisotropy is more general than that due to a magnetic field and we coin the former “inverse anisotropic catalysis”. Finally, we observe that any amount of anisotropy changes the IR physics substantially: the geometry is AdS4 × ℝ up to small corrections, confinement is present only up to a certain scale, and the particles acquire finite widths.

Electromagnetic and axial current form factors and spectroscopy of three-flavor holographic baryons

We present an analysis of the three-flavor holographic model of QCD associated to a $D4/D8$ brane configuration, with symmetry breaking induced by a worldsheet instanton associated to a closed loop connecting $D4-D8-D6-\overline{D8}$. We calculate the electromagnetic and axial couplings of all octet and decuplet baryons, as well as several negative parity excitations, with and without symmetry breaking effects, and demonstrate qualitative and quantitative agreement with many available experimental measurements, with marked improvement over the analogous two-flavor models.

Criticality of QCD in a holographic QCD model with critical end point * * Supported by the NSFC (11725523, 11735007, 11805084 and 11261130311) (CRC 110 by DFG and NSFC)

The thermodynamics of strongly interacting matter near the critical end point are investigated in a holographic QCD model, which can describe the QCD phase diagram in plane qualitatively. Critical exponents along different axes ( ) are extracted numerically. It is given that , , , and , which is similar to the three-dimensional Ising mean-field approximation and previous holographic QCD model calculations. We also discuss the possibilities to go beyond the mean field approximation by including the full back-reaction of the chiral dynamics in the holographic framework.

Theoretical Studies of Heavy Ion Collisions via Holography

Applications of holographic bottom-up QCD models to the studies of Heavy Ion Collisions (HIC) are discussed.

Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model, with two, three degenerate flavors (Nf = 2, 3) and two light plus one heavier flavor (Nf = 2 + 1). It is shown that in quark mass plane (mu/d − ms) chiral phase transition is second order at a certain critical line, by which the whole plane is divided into first order and crossover regions. The critical exponents β and δ, describing critical behavior of chiral condensate along temperature axis and light quark mass axis, are extracted both numerically and analytically. The model gives the critical exponents of the values beta =frac{1}{2},delta =3 and beta =frac{1}{3},delta =3 for Nf = 2 and Nf = 3 respectively. For Nf = 2 + 1, in small strange quark mass (ms) region, the phase transitions for strange quark and u/d quarks are strongly coupled, and the critical exponents are beta =frac{1}{3},delta =3 ; when ms is larger than ms,t = 0.290 GeV, the dynamics of light flavors (u, d) and strange quarks decoupled and the critical exponents for ūu and overline{d}d becomes beta =frac{1}{2},delta =3 , exactly the same as Nf = 2 result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at ms,t = 0.290 GeV, at which beta =frac{1}{4},delta =5 . In some sense, the current results is still at mean field level, and we also showed the possibility to go beyond mean field approximation by including the higher power of scalar potential and the temperature dependence of dilaton field, which might be reasonable in a full back-reaction model. The current study might also provide reasonable constraints on constructing a realistic holographic QCD model, which could describe both chiral dynamics and glue-dynamics correctly.

Deep learning and holographic QCD

We apply the relation between deep learning (DL) and the AdS/CFT correspondence to a holographic model of QCD. Using a lattice QCD data of the chiral condensate at a finite temperature as our training data, the deep learning procedure holographically determines an emergent bulk metric as neural network weights. The emergent bulk metric is found to have both a black hole horizon and a finite-height IR wall, so shares both the confining and deconfining phases, signaling the cross-over thermal phase transition of QCD. In fact, a quark antiquark potential holographically calculated by the emergent bulk metric turns out to possess both the linear confining part and the Debye screening part, as is often observed in lattice QCD. From this we argue the discrepancy between the chiral symmetry breaking and the quark confinement in the holographic QCD. The DL method is shown to provide a novel data-driven holographic modeling of QCD, and sheds light on the mechanism of emergence of the bulk geometries in the AdS/CFT correspondence.

Subregion complexity and confinement–deconfinement transition in a holographic QCD model

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 Cˆ versus the subregion length scale ℓ, we find that for both cases, Cˆ always experiences a discontinuity at certain critical value ℓc in confinement phases, while it is always continuous in deconfinement phases. This property may be seen as a signal to characterize confinement or deconfinement phases. The behavior of Cˆ versus the temperature and chemical potential is also investigated and our results show that Cˆ exhibits behavior characterizing the type of the transition. That is, it experiences a discontinuity at the transition temperature for μ<μc where first-order confinement–deconfinement phase transition happens, while it is always continuous for μ>μc where the transition turns into a turnover. These results imply that the renormalized holographic complexity density may be used as a good parameter to characterize the corresponding phase structures.

QCD domain walls, Chern-Simons theories and holography

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 supported by the string theory construction.

Universal magnetoresponse in QCD and mathcal{N}=4 SYM

Using recent lattice data on the thermodynamics of QCD in the presence of a background magnetic field, we show that the ratio of transverse to longitudinal pressure exhibits, to good accuracy, a simple scaling behavior over a wide range of temperature and magnetic field, essentially depending only on the ratio T/sqrt{B} . We compare this QCD response to the corresponding magnetoresponse in maximally supersymmetric Yang Mills theory. Given suitable calibrations defining the comparison, we find excellent agreement. This may be viewed as a further test of the applicability of holographic models for hot QCD.

Nonminimal coupling contribution to DIS at low x in Holographic QCD

We consider the effect of including a non-minimal coupling between a $U(1)$ vector gauge field and the graviton Regge trajectory in holographic QCD models. This coupling describes the QCD interaction between the quark bilinear electromagnetic current and the Pomeron. We test this new coupling against DIS data at low Bjorken $x$ and obtain an excellent fit with a chi squared of 1.1 over a very large kinematical range in the photon virtuality $Q^2<400 \ {\rm GeV}^2$ and for $x<10^{-2}$. The scale of the new dimension full coupling, which arises from integrating higher spin fields, is of order $6\ {\rm GeV}$. This value matches precisely the expectations from effective field theory, which indicate that such corrections are controlled by the mass gap between the spin two and spin four glueballs that are described holographically by the graviton and spin four field in the graviton Regge trajectory, respectively

Holographic QCD in the Veneziano Limit at a Finite Magnetic Field and Chemical Potential.

We investigate QCD-like gauge theories at strong coupling at a finite magnetic field B, temperature T, and quark 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 a finite μ. In particular, we observe that inverse magnetic catalysis exists only for small values of the chemical potential. The speed of sound in this holographic quark-gluon plasma exhibits interesting dependence on the thermodynamic parameters.