Soft-wall Holographic Model Research Articles

Hawking-Page transition in holographic QCD at finite density

We study the confinement/deconfinement transition of QCD matter for a quark-gluon plasma at finite density using AdS/QCD duality. In order to determine the critical temperature and its dependence on the quark chemical potential, the semi-classical Hawking-Page approach is considered for a charged AdS black hole. The result obtained is consistent with the QCD phase diagram, with the critical temperature decreasing as the chemical potential increases. Using the soft wall holographic model, the value of quark density in which the phase transition occurs at zero temperature is estimated. For higher densities the QCD matter is deconfined, independent of the temperature.

Hadronic light-by-light scattering contributions to (g−2)μ from axial-vector and tensor mesons in the holographic soft-wall model

We compute the light axial-vector and tensor meson two-photon transition form factors in the soft-wall holographic model of quantum chromodynamics (QCD) in the flavor-symmetric case. They are used to evaluate the axial-vector and tensor meson contributions to the anomalous magnetic moment of the muon via the hadronic light-by-light scattering process. As expected, these contributions are smaller than the one from pseudoscalar mesons. The result for axial-vector mesons is higher than the value found in other approaches. Published by the American Physical Society 2024

Axial-vector form factor of nucleons at finite temperature from the AdS/QCD soft-wall model

The axial-vector form factor of the nucleons is studied at a finite temperature using the holographic soft-wall model with the thermal dilaton field. We use the bulk interaction action known from the zero temperature case and apply the profile functions of fields thermalized by the interaction with the thermal dilaton field. The dependence of the axial form factor on the square of the transferred momentum and the temperature is plotted for the ground and excited states of the nucleons.

On incorporation of heavy-quark mass into soft-wall holographic models

In this paper, we consider the soft-wall holographic model with the linear dilaton background. The model leads to a Hydrogen-like meson spectrum which can be interpreted as the static limit with very large quark masses when the Coulomb interaction dominates. The mass scale introduced by the linear dilaton is matched to the quark mass. The resulting model is analyzed for the scalar, vector and tensor cases. The electromagnetic coupling constants predicted by the model are decreasing with the radial number in contrast to the soft-wall model with quadratic dilaton where these couplings represent a universal constant. The given prediction is qualitatively consistent with the corresponding experimental data in vector quarkonia. The proposed model can thus be used as a constituent part of more elaborated holographic models for heavy quarkonia. A particular example of such a model is put forward.

A second Higgs near 0.5 TeV from bottom-up holographic modeling of beyond the Standard Model strong sector

One of the simplest extensions of the Standard Model (SM) consists in adding a scalar singlet. This second Higgs boson is able to solve several fundamental problems of SM. Additional scalar particles arise naturally in composite Higgs scenarios in which some confining “strong sector” beyond the SM drives the electroweak symmetry breaking. The underlying strongly coupled gauge theory may be similar to QCD and could be modeled holographically. We construct a bottom-up holographic model for description of the spectrum of composite Higgs particles. The model is based on the holographic Soft Wall model and the Wilson confinement criterion. The constructed model predicts the existence of a second Higgs boson with a mass of about 515 GeV.

π0,η,η′ two-photon transition form factors in the holographic soft-wall model and contributions to (g−2)μ

We compute the two-photon transition form factors of the light pseudoscalar π0, η and η′ mesons in a soft-wall holographic model of QCD with a solution of the U(1)A problem. We compare the results with the experimental data in different ranges of photon virtualities. The obtained transition form factors are used to determine the π0, η and η′ pole terms in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.

Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum

It is well known that the soft-wall holographic model for QCD successfully reproduces not only the linear Regge spectrum, but also, via the holographic Wilson confinement criterion, the “linear plus Coulomb” confinement potential, which is similar to the Cornell potential. This property could be interpreted as a holographic counterpart of the hadron string picture, where the linearly rising potential and Regge-like spectrum are directly related. However, such a relation does not exist in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up holographic models. The standard soft-wall model is merely a particular representative of this class. This fact is relatively unknown, so we provide a comprehensive discussion of the point. As an example, we consider a soft-wall-like model with linear dilaton background in the metric. This model leads to a hydrogen-like spectrum. A “linear plus Coulomb” confinement potential within this model is calculated. The calculation of renormalized potential at short distances turns out to be complicated by a new subtlety that was skipped in general discussions of the issue existing in the literature. However, the confinement potential of the model is shown to be not very different from the potential obtained in the standard soft-wall model with a quadratic background.

Cornell potential in generalized soft wall holographic model

We derive and analyze the confinement potential of the Cornell type within the framework of the generalized soft wall holographic model that includes a parameter controlling the intercept of the linear Regge spectrum. In the phenomenology of Regge trajectories, this parameter is very important for the quantitative description of experimental data. Our analysis shows that the ‘linear plus Coulomb’ confinement potential obtained in the scalar channel is quantitatively consistent with the phenomenology and lattice simulations while the agreement in the vector channel is qualitative only. This result indicates the key role of the vacuum scalar sector in the formation of the confinement potential. As a by-product the overall consistency of our holographic description of confinement potential seems to confirm the glueball nature of the scalar meson f 0(1500).

Gluon string breaking and meson spectrum in the holographic Soft Wall model

We propose a general method for finding a string-like meson spectrum which is based on a certain condition for the breaking of closed gluon string. A model is constructed that successfully realizes the proposed method. The model is based on the holographic Soft Wall model for QCD and the use of the Wilson confinement criterion. We applied our approach to the vector and scalar cases and obtained numerical predictions for the intercepts of corresponding Regge like radial meson spectra. A good agreement is obtained both with the existing experimental data and with some other known phenomenological approaches. Remarkably, our closed string breaking condition has two branches. We argue that they should correspond to states of opposite parity. The Wilson confinement criterion leads then to a natural mass splitting between parity partners. The constructed model represents thus the first example of bottom-up holographic model in which the effects of chiral symmetry breaking can emerge automatically, i.e., without additional assumptions taken outside of the holographic approach.

Pseudoscalars and the η′ in the holographic soft-wall model

Pseudoscalar mesons and glueballs are studied in a model based on the AdS/QCD correspondence. Glueball masses are obtained in the pure-gauge case, while the mixing between pseudoscalar glueballs and singlet pseudoscalar mesons produces the expected mass of the η′ meson. The topological susceptibility is computed as a function of the quark mass. The model reproduces partial conservation of axial current, the anomaly equation, and the Witten-Veneziano relation.

Spontaneous chiral symmetry breaking in holographic soft wall models

We investigate nonlinear extensions of the holographic soft wall model proposed by Karch et al. [Phys. Rev. D 74, 015005 (2006)] including nonminimal couplings in the five-dimensional action. The nonminimal couplings bring a new parameter ${a}_{0}$ which controls the transition between spontaneous and explicit symmetry breaking near the limit of massless quarks (the chiral limit). In the physical region (positive quark mass), we show that above a critical value of the parameter ${a}_{0}$ the chiral condensate $⟨\overline{q}q⟩$ is finite in the chiral limit, signifying spontaneous chiral symmetry breaking. This result is supported by the lightest states arising in the spectrum of the pseudoscalar mesons, which become massless in the chiral limit and are therefore intrepreted as Nambu-Goldstone bosons. Moreover, the decay constants of the pseudoscalar mesons also support this conclusion, as well as the Gell-Mann-Oakes-Renner relation satisfied by the lightest states. We also calculate the spectrum of scalar, vector, and axial-vector mesons with their corresponding decay constants. We describe the evolution of masses and decay constants with the increasing of the quark mass, and for the physical mass, we compare our results against available experimental data. Finally, we do not find instabilities in our model for the physical region (positive quark mass).

The Effect of Higher Dimensional QCD Operators on the Spectroscopy of Bottom-Up Holographic Models

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 have not been taken into account in virtually any 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 soft wall holographic model, and in the hard wall holographic model, they result in a proliferation of excited states. The considered model can be viewed as the first analytical toy model predicting a one-to-one mapping of the excited meson states to definite QCD operators, to which they prefer to couple.

Finite density effects on chiral symmetry breaking in a magnetic field in 2+1 dimensions from holography

In this work, we study finite density effects in spontaneous chiral symmetry breaking as well as chiral phase transition under the influence of a background magnetic field in $2+1$ dimensions. For this purpose, we use an improved holographic soft wall model based on an interpolated dilaton profile. We find inverse magnetic catalysis at finite density. We observe that the chiral condensate decreases as the density increases, and the two effects (addition of magnetic field and chemical potential) sum up, decreasing even more the chiral condensate.

Towards reconciling the holographic and lattice descriptions of radially excited hadrons

Within the framework of AdS/QCD models, the spectra of radially excited hadrons are identified with towers of Kaluza–Klein (KK) states in a putative dual theory. The infinite number of KK states is indispensable to provide correct high energy asymptotics of correlation functions in QCD. It is known, however, that the KK modes of dual theory must be qualitatively different from real hadrons. And what is more important, the radially excited states appear in lattice calculations not as ”excitations” of some ground state, but rather as independent states coupled to higher dimensional QCD operators – the larger is a basis of interpolating operators, the larger set of states can be resolved. A question arises whether is it possible to reconcile the holographic and lattice descriptions of radially excited hadrons? We propose a new phenomenological ”consistency test” for bottom-up holographic models: If the KK spectrum of massive 5D fields dual to higher dimensional operators in QCD coincides with the conventional radial KK spectrum, then the holographic KK states can be identified with real excited mesons in the large-N_c limit of QCD. We demonstrate that the Soft Wall holographic model passes this test while the Hard Wall model does not.

Nonlinear realization of chiral symmetry breaking in holographic soft wall models

We investigate nonlinear extensions of the holographic soft wall model proposed by Karch et al. [Phys. Rev. D 74, 015005 (2006)] with a positive quadratic dilaton. We consider a Higgs potential for the tachyonic field that brings a more natural realization of chiral symmetry breaking in the infrared regime. Utilizing the $\mathrm{AdS}/\mathrm{CFT}$ dictionary and holographic renormalization, we find the chiral condensate as a function of the quark mass. The nonlinearity of the Higgs potential leads to a nonlinear relation between the chiral condensate and the quark mass. Solving the effective Schr\"odinger equations for the field perturbations, we estimate meson masses and decay constants and evaluate their dependence on the quark mass. In the axial and pseudoscalar sector we find an interesting behavior for the decay constants as the quark mass increases. We also investigate the effect of a five-dimensional running mass for the tachyonic field. We conclude that nonlinear soft wall models with a Higgs potential for the tachyon and a positive quadratic dilaton do not provide spontaneous symmetry breaking in the chiral limit.

Deconfinement Temperature in AdS/QCD from the Spectrum of Scalar Glueballs

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 fixing parameters of holographic models. The observed stability in the former case clearly favors the choice of the glueball channel for thermodynamic predictions in AdS/QCD models, with the scalar glueball trajectory being taken from lattice simulations and used as a basic input in improved versions of the Soft Wall holographic model.

Estimates of the Deconfinement Temperature in ADS/QCD

We study various methods for estimating the deconfinement temperature in nondynamical bottom-up AdS/QCD models in detail. We show that although there are many different possibilities to define the holographic parameters, certain reasonable theoretical and phenomenological restrictions on holographic models lead to realistic and rather stable predictions for the range of temperatures in the deconfinement crossover region at small baryon densities. In particular, we argue that the most successful approach is to take the scalar glueball trajectory from lattice simulations as a basic input in an improved version of the soft-wall holographic model.

Dynamical versions to the holographic softwall model: Using type IIB superstring backgrounds via AdS/CFT correspondence in hadronic physics

In this paper we will show some applications achieved within type IIB superstring backgrounds since the emergence of the AdS/CFT correspondence. This correspondence relates a super Yang-Mills (SYM) theory, with strong coupling, and a type IIB superstring theory, with weak coupling. The use of the AdS/CFT correspondence allows us to investigate many aspects of hadronic physics described by QCD outside the perturbative regime, for example, glueball masses and the Regge trajectories related to the pomeron and the odderon. Throughout the text we will deal with the AdS/CFT correspondence within the two dynamical versions to the holographic softwall model.

Scalar and higher even spin glueball masses from an anomalous modified holographic model

In this work, within an anomalous modified holographic softwall model, we calculate analytically the masses of the scalar glueball with its radial excitations and higher even glueball spin states, with , from a single mass equation. Using this approach we achieved a unified treatment for both scalar and high even spin glueballs masses. Furthermore, we also obtain the Regge trajectory associated with the pomeron compatible with other approaches.

Meson spectrum for arbitrary twist in soft-wall holographic model

The Regge spectrum of soft-wall holographic model is generalized to the case of arbitrary twist. Combining this result with the light-front holographic QCD, one arrives at a broad hydrogen-like degeneracy of the same sort as the degeneracy observed experimentally in the spectrum of light mesons.