Soft-wall Model Research Articles

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).

Temperature dependence of ρ meson-nucleon coupling constant from the AdS/QCD soft-wall model

We investigate the dependence of the $\rho$ meson-nucleon coupling constant on the temperature of the medium using the soft-wall model of AdS/QCD. The finite temperature profile functions for the vector and fermion fields are applied to the model having a thermal dilaton field. The interaction Lagrangian in the bulk between these fields is written as in zero temperature case and includes minimal- and magnetic-type interactions. The temperature dependence of the $g_{\rho NN}(T)$ coupling constant and its terms are plotted. We observe that the coupling constant and its separate terms become zero at the medium temperature near the Hawking temperature of phase transition.

Meson and glueball spectroscopy within the graviton soft wall model

The graviton soft wall (GSW) model provides a unified description of the scalar glueball and meson spectra with a unique energy scale. This success has led us to extend the analysis to the description of the spectra of other hadrons. We use this model to calculate masses of the odd and even ground states of glueballs for various spins, and show that the GSW model is able to reproduce the Regge trajectory of these systems. In addition, the spectra of the $\ensuremath{\rho}$, ${a}_{1}$ and $\ensuremath{\eta}$ mesons will be addressed. Results are in excellent agreement with current experimental data. Furthermore such an achievement is obtained without any additional parameters. Indeed, the only two parameters appearing in these spectra are those that were previously fixed by the light scalar meson and glueball spectra. Finally, in order to describe the $\ensuremath{\pi}$ meson spectrum, a suitable modification of the dilaton profile function has been included in the analysis to properly take into account the Goldstone realization of chiral symmetry. The present investigation confirms that the GSW model provides an excellent description of the spectra of mesons and glueballs with only a small number of parameters unveiling a relevant predicting power.

U(1)A axial anomaly, η′ , and topological susceptibility in the holographic soft-wall model

The singlet pseudoscalar sector of light mesons is investigated in the soft-wall model, a bottom-up approach to the AdS/QCD correspondence. The $\eta^\prime$ mass results from the mixing among the fields dual to the axial current, pseudoscalar current and the $G\tilde G$ operator. The topological susceptibility is computed for any quark mass, and the Witten-Veneziano relation is obtained in the large $N_c$ limit.

QCD phase diagram with a background magnetic field in an improved soft-wall AdS/QCD model

We studied the magnetic effects on the chiral transition and the melting properties of vector and axial-vector mesons in the improved soft-wall AdS/QCD model under a charged magnetic background, which is solved perturbatively from an Einstein–Maxwell system with a negative cosmological constant. The phase diagrams for both chiral transition and meson melting have been obtained. We show that the inverse magnetic catalysis emerged naturally in the improved soft-wall model. We also find that the magnetic field can induce meson melting, at least for the vector and axial-vector mesons, in our holographic setup.

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.

Properties of protons in nuclear medium with AdS/QCD model with a quadratic modified dilaton

A modified version of the usual AdS/QCD soft wall model with quadratic dilaton is presented to study proton properties inside the atomic nucleus. We suggest a dilaton that catches the variation of the proton mass inside nuclei, called nuclear dilaton, and with this, we calculated electromagnetic form factors and magnetic moments for protons inside the atomic nucleus.

A New Approach to Radial Spectrum of Hadrons in Bottom-up Holographic QCD

Within the AdS/CFT correspondence, for description of $\mathcal{N}=4$ super Yang-Mills theory in four dimensions one needs not only low-energy supergravity on AdS$_5$ but also the whole infinite tower of massive Kaluza-Klein (KK) states on AdS$_5\times$S$_5$ which appear after the KK-compactification on five-dimensional sphere. The latter aspect is usually ignored in phenomenological AdS/QCD models. The emerging massive 5D fields on AdS$_5$ are dual to higher-dimensional operators in 4D gauge theory, with masses being known polynomial functions of canonical dimensions of these operators. Motivated by this observation, we propose to calculate the spectrum of radially excited hadrons in bottom-up holographic QCD models as spectrum of zero KK modes of massive 5D fields dual to higher dimensional operators in QCD. A relevant physical motivation is suggested. The radial states with growing masses are then enumerated by growing dimensions of interpolating QCD operators. We tested the proposal in the Soft Wall and Hard Wall holographic models in the sector of light mesons. The spectrum of Soft Wall model turns out to be unchanged in the new description. But in the Hard Wall model, our approach is shown to lead to a much better phenomenological spectrum of vector radial excitations than the traditional description.

Scalar spectrum in a graviton soft wall model

In this study we present a unified phenomenological analysis of the scalar glueball and scalar meson spectra within an AdS/QCD framework in the bottom up approach. For this purpose we generalize the recently developed graviton soft-wall (GSW) model, which has shown an excellent agreement with the lattice QCD glueball spectrum, to a description of glueballs and mesons with a unique energy scale. In this scheme, dilatonic effects, are incorporated in the metric as a deformation of the AdS space. We apply the model also to the heavy meson spectra with success. We obtain quadratic mass equations for all scalar mesons while the glueballs satisfy an almost linear mass equation. Besides their spectra, we also discuss the mixing of scalar glueball and light scalar meson states within a unified framework: the GSW model. To this aim, the light-front (LF) holographic approach, which connects the mode functions of AdS/QCD to the LF wave functions, is applied. This relation provides the probabilistic interpretation required to properly investigate the mixing conditions.

Thermodynamics of soft wall model of AdS/QCD in Einstein–Maxwell–Gauss–Bonnet gravity

We investigate the thermodynamics of the confinement–deconfinement transition in the soft wall model of QCD with Gauss–Bonnet corrections using anti-de Sitter – conformal field theory (AdS/CFT) correspondence. In bulk AdS space–time the transition is geometric and is known as Hawking–Page transition. The Hawking–Page transition between two geometries, namely, charged AdS black hole and thermally charged AdS, have been studied with Gauss–Bonnet corrections up to first order. The Gauss–Bonnet coupling modifies the transition temperature of the system, but qualitative features remain unchanged. We obtain the curves between chemical potential and transition temperature for different values of Gauss–Bonnet couplings. We find that there exists a point in the μ–T plane where lines with different values of Gauss–Bonnet coupling cross. This point may be the onset of the transition from first-order to cross over behavior. The results are compared with that of the hard wall model.

Nonlinear Regge trajectories with AdS/QCD

In this work, we consider a non-quadratic dilaton $\Phi(z)=(\kappa\,z)^{2-\alpha}$ in the context of the static soft wall model to describe the mass spectrum of a wide range of vector mesons from the light up to the heavy sectors. The effect of this non-quadratic approach is translated into non-linear Regge trajectories with the generic form $M^2=a\,(n+b)^\nu$. We apply this sort of fits for the isovector states of $\omega$, $\phi$, $J/\psi$ and $\Upsilon$ mesons and compare with the corresponding holographic duals. We also extend these ideas to the heavy-light sector by using the isovector set of parameters to extrapolate the proper values of $\kappa$ and $\alpha$ through the average constituent mass $\bar{m}$ for each mesonic specie considered. In the same direction, we address the description of possible non-$q\,\bar{q}$ candidates using $\bar{m}$ as a holographic threshold, associated with the structure of the exotic state, to define the values of $\kappa$ and $\alpha$. We study the $\pi_1$ mesons in the light sector, and the $Z_c$, $Y$ and $Z_b$ mesons in the heavy sector as possible exotic vector states. Finally, the RMS error for describing these twenty-seven states with fifteen parameters (four values for $\kappa$ and $\alpha$ respectively and seven values for $\bar{m}$) is $12.61\%$.

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.

Light pseudoscalar and axial spectroscopy using AdS/QCD modified soft wall model

We describe the mass spectrum of light pseudoscalar and axial mesons in the context of the modified soft wall model with an extra UV cutoff. In order to include the pseudoscalar and axial states, we define an anomalous dimension that shifts the conformal dimension of the non-interacting bulk fields such that the parity behavior of those states is included, thus inducing chiral symmetry breaking. This idea contrasts with the usual approach that uses interacting scalar, vector and axial bulk fields to give rise the spectrum. Using the extra UV cutoff approach, we can fit six η and six a1 organized in radial trajectories with an RMS error close to 21.1%. We also confirm that chiral symmetry is restored in this model after checking that highly excited ρ and a1 states become degenerate.

Probing AdS/QCD backgrounds with semi-classical strings

New AdS/QCD backgrounds have been proposed to describe the spectrum of heavy vector mesons via the implementation of additional energy scales on the bulk geometry of the soft-wall model. The extra energy scales are needed to include the decay constants of hadronic states when describing the radial excitations of the heavy meson. Here we analyze one model that introduces an ultraviolet cutoff on Anti-de Sitter space and a model that considers a dilaton profile modified by the addition of an extra term and no cutoff. For each one of these two models we consider the presence of a semi-classical string in the bulk that is dual to a static and infinitely heavy meson. We compute the expected value of the Wilson loop operator using the holographic dictionary and obtain the dual potential for the static pair. For the model with modified dilaton profile the on-shell string action presents a peculiar ultraviolet divergence, a compatible regularization is discussed and a new subtraction scheme is used. We consider the case of finite temperature and determine how the dissociation temperature of the heavy meson is affected by the additional energy scales.

Константа взаимодействия вектор-мезона с дельта-барионами в модели мягкой стены AдС/КХД

Константа взаимодействия вектор-мезона с дельта-барионами в модели мягкой стены AдС/КХД

Holographic description of chiral symmetry breaking in a magnetic field in 2+1 dimensions with an improved dilaton

We consider a holographic description of the chiral symmetry breaking in an external magnetic field in -dimensional gauge theories from the softwall model using an improved dilaton field profile given by . We find inverse magnetic catalysis for B < Bc and magnetic catalysis for B > Bc, where Bc is the pseudocritical magnetic field. The transition between these two regimes is a crossover and occurs at , which depends on the fermion mass and temperature. We also find spontaneous chiral symmetry breaking (the chiral condensate ) at T = 0 in the chiral limit () and chiral symmetry restoration for finite temperatures. We observe that changing the k parameter of the dilaton profile only affects the overall scales of the system such as Bc and σ. For instance, by increasing k one sees an increase of Bc andσ. This suggests that increasing the parameters k1 and k2 will decrease the values of Bc and σ.

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.

Deep inelastic scattering from string/gauge duality with soft IR cutoff and exponentially small Bjorken parameter

In this work we use the string/gauge duality within the Softwall Model (SW). In this model a dilaton field is introduced in the action for the fields playing the role of a soft infrared (IR) cutoff. The SW model is very useful as it provides linear Regge trajectories for mesons. Here, using a 10–dimensional SW model, we calculate the corresponding structure functions for deep inelastic scattering (DIS) in which electrons are scattered off hadrons in a kinematical regime where the hadrons are broken apart, with high virtuality q, in the exponentially small x (Bjorken parameter) regime. Our results for this regime are consistent with those achieved using other holographic and non-holographic approaches.

Axial Vector-Meson–Nucleon Interaction Constant in the AdS/QCD Soft Wall Model

This work investigates the interaction of an axial vector-meson with nucleons in the AdS/QCD soft wall model. The axial vector fields have been determined inside the anti-de Sitter (AdS) space with the help of gauge fields with left and right chiral symmetries. In addition, a pseudoscalar field has been introduced inside the AdS space to break the chiral symmetry. A Lagrangian for these fields has been introduced inside the AdS space and the profile functions which are solutions of the equation of motion have been found. In accordance with AdS/CFT, the interaction constant of the axial vector-meson with the nucleons has been obtained as an integral over the additional dimension. The main task of this work was to find numerical values of the interaction constant of the axial vector-meson with the nucleons in the AdS/QCD soft wall model. With the help of the computer program Mathematica 7, these values were determined. A comparison of the theoretical and experimental data has revealed significant agreement of the results.