Soft-wall Models Research Articles

Comparison between holographic deformed AdS and soft wall models for fermions

Comparison between holographic deformed AdS and soft wall models for fermions

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 holographic bottom-up description of light nuclide spectroscopy and stability

This work explores a holographic proposal to describe light nuclide spectroscopy by considering extensions to the well-known bottom-up AdS/QCD proposals, the hardwall and softwall models. We also propose an alternative description inspired by the Woods-Saxon potential. We find the static dilaton associated with this potential in this Wood-Saxon-like model. We compute the nuclide spectra finding that, despite their pure AdS/QCD origin, hardwall and softwall, as monoparametric models, have good accuracy and precision since the RMS error is near 11% and 4% respectively. In the case of the Wood-Saxon model, the RMS was around 1%. We also discuss configurational entropy as a tool to categorize which model is suitable to describe nuclides in terms of stability. We found that configurational entropy resembles a stability line, independent from nuclear spin, for symmetric light nuclides when considering softwall and Wood-Saxon-like models. For the hardwall case, configurational entropy, despite increasing with the constituent number, depends on the nuclear spin. Thus, the Woods-Saxon-like model emerges as the best choice to describe light nuclide spectroscopy in the bottom-up scenario.

Hadronic vacuum polarization contribution to the muon g−2 in holographic QCD

We evaluate the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon with two light flavors in minimal hard-wall and soft-wall holographic QCD models, as well as in simple generalizations thereof, and compare with the rather precise results available from dispersive and lattice approaches. While holographic QCD cannot be expected to shed light on the existing small discrepancies between the latter, this comparison in turn provides useful information on the holographic models, which have been used to evaluate hadronic light-by-light contributions where errors in data-driven and lattice approaches are more sizable. In particular, in the hard-wall model that has recently been used to implement the Melnikov-Vainshtein short-distance constraint on hadronic light-by-light contributions, a matching of the hadronic vacuum polarization to the data-driven approach points to the same correction of parameters that has been proposed recently in order to account for next-to-leading order effects.

Partonic behavior of string scattering amplitudes from holographic QCD models

We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s. In the fixed angle approximation we find in the hard and soft wall models that mathcal{A} ∼ s2−∆/2 whereas in Witten’s model mathcal{A} ∼ s3−∆/2 and mathcal{A} ∼ s7/3−2∆/3 for the 11D and 10D formulations, respectively. In the Regge regime mathcal{A} ∼ s2t−2+α (log s/t)−1+α where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [ mathcal{A} ] ∼ s−1, Im [ mathcal{A} ] ∼ sα. We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.

Towards a theory of bottom-up holographic models for linear Regge trajectories of light mesons

We advance in constructing a bottom-up holographic theory of linear meson Regge trajectories that generalizes and unites into one logical framework various bottom-up holographic approaches proposed in the past and scattered in the literature. The starting point of the theory is a quadratic in fields holographic five-dimensional action in which the Poincaré invariance along the holographic coordinate is violated in the most general way compatible with the linear Regge behavior of the discrete spectrum in four dimensions. It is further demonstrated how different Soft Wall (SW) like holographic models existing in the literature plus some new ones emerge from our general setup. Various interrelations between the emerging models are studied. These models include the known SW models with different sign in the exponential background, the SW models with certain generalized backgrounds, with modified metrics, and No Wall models with 5D mass depending on the holographic coordinate in a simple polynomial way. We argue that this dependence allows to describe the effects caused by the main non-local phenomena of strongly coupled 4D gauge theory, the confinement and chiral symmetry breaking, in terms of a local 5D dual field theory in the AdS space. We provide a detailed comparison of our approach with the Light Front holographic QCD, with the spectroscopic predictions of the dual Veneziano like amplitudes, and with the experimental Regge phenomenology. We apply our general approach to a holographic study of confinement, chiral symmetry breaking, and the pion form factor.

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).

Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography

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, showing the evidence of the restored chiral symmetry in hadronic spectrum level. Extending to finite quark mass, pion masses increase with quark mass. Further, it is more interesting to observe that the pole masses of pions decrease with temperature below $T_c$, which agrees with the analysis in Phys.Rev.Lett.88(2002)202302. Meanwhile, symmetry restoration above $T_c$ could be seen in the spectra of scalar and pseudo-scalar mesons. With finite temperature and isospin chemical potential $\mu_I$, it is shown that the masses of charged pions would split. The mass of positive charged pion $\pi^+$ decreases almost linearly to zero when $\mu_I$ grows to $\mu_{I}^c$, where pion condensation starts to form. This reveals the Goldstone nature of $\pi^+$ after pion superfluidity transition, which are closely related to the experimental observation.

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.

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.

Double parton correlations in mesons within AdS/QCD soft-wall models: a first comparison with lattice data

Double parton distribution functions (dPDFs), entering the double parton scattering (DPS) cross section, are unknown fundamental quantities encoding new interesting properties of hadrons. Here, the pion dPDFs are investigated within different holographic QCD quark models in order to access their basic features. Results of the calculations obtained within the AdS/QCD soft-wall approach, have been compared with predictions of lattice QCD evaluations of the pion two-current correlation functions. The present analysis confirms that double parton correlations, affecting dPDFs, are very important and not direct accessible from generalised parton distribution functions and electromagnetic form factors. The comparison between lattice data and quark model calculations unveils the relevance of the contributions of high partonic Fock states in the pion. Nevertheless, by using a complete general procedure, results of lattice QCD have been used, for the first time, to estimate the mean value of the so called sigma _{eff}, a relevant experimental observable for DPS processes. In addition, the results of the first calculations of the rho meson dPDFs are discussed in order to make predictions.

Chiral symmetry breaking and restoration in 2+1 dimensions from holography: Magnetic and inverse magnetic catalysis

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 symmetry breaking for both models. Interestingly, for $B=0$ in the softwall model we found a nontrivial expectation value for the chiral condensate.

Magnetic catalysis and inverse magnetic catalysis in ( 2+1 )-dimensional gauge theories from holographic models

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.

A perturbative RS I cosmological phase transition

We identify a class of Randall–Sundrum type models with a successful first order cosmological phase transition during which a 5D dual of approximate conformal symmetry is spontaneously broken. Our focus is on soft-wall models that naturally realize a light radion/dilaton and suppressed dynamical contribution to the cosmological constant. We discuss phenomenology of the phase transition after developing a theoretical and numerical analysis of these models both at zero and finite temperature. We demonstrate a model with a TeV-Planck hierarchy and with a successful cosmological phase transition where the UV value of the curvature corresponds, via AdS/CFT, to an N of 20, where 5D gravity is expected to be firmly in the perturbative regime.

Gravitational waves generated from the cosmological QCD phase transition within AdS/QCD

We study the gravitational waves produced by the collision of the bubbles as a probe for the cosmological first order QCD phase transition, considering heavy static quarks. Using AdS/QCD and the correspondence between a first order Hawking–Page phase transition and confinement–deconfinement phase transition, we find the spectrum and the strain amplitude of the gravitational wave within the hard and soft wall models. We postulate the duration of the phase transition corresponds to the evaporation time of the black hole in the five dimensional dual gravity space, and thereby obtain a bound on the string length in the space and correspondingly on the duration of the QCD phase transition. We also show that IPTA and SKA detectors will be able to detect these gravitational waves, which can be an evidence for the first order deconfinement transition.

Two-gluon and trigluon glueballs from dynamical holography QCD**Supported by the NSFC (11175251, 11621131001), DFG and NSFC (CRC 110), CAS Key Project KJCX2-EW-N01, K.C.Wong Education Foundation, and Youth Innovation Promotion Association of CAS

We study the scalar, vector and tensor two-gluon and trigluon glueball spectra in the framework of the 5-dimension dynamical holographic QCD model, where the metric structure is deformed self-consistently by the dilaton field. For comparison, the glueball spectra are also calculated in the hard-wall and soft-wall holographic QCD models. In order to distinguish glueballs with even and odd parities, we introduce a positive and negative coupling between the dilaton field and glueballs, and for higher spin glueballs, we introduce a deformed 5-dimension mass. With this set-up, there is only one free parameter from the quadratic dilaton profile in the dynamical holographic QCD model, which is fixed by the scalar glueball spectra. It is found that the two-gluon glueball spectra produced in the dynamical holographic QCD model are in good agreement with lattice data. Among six trigluon glueballs, the produced masses for 1±− and 2−− are in good agreement with lattice data, and the produced masses for 0−−, 0+− and 2+− are around 1.5 GeV lighter than lattice results. This result might indicate that the three trigluon glueballs of 0−−, 0+− and 2+− are dominated by the three-gluon condensate contribution.

No inverse magnetic catalysis in the QCD hard and soft wall models

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 holographically as a function of the applied magnetic field and demonstrate that this model does not exhibit inverse magnetic catalysis at the level of the chiral transition. The quest for a holographic QCD model that qualitatively describes the inverse magnetic catalysis at finite temperature is thus still open. Throughout this work, we pay special attention to the different holographic parameters and we attempt to fix them by making the link to genuine QCD as close as possible. This leads to several unanticipated and so far overlooked complications (such as the relevance of an additional length scale in the confined geometry) that we discuss in detail.

On dilatons and the LHC diphoton excess

We study soft wall models that can embed the Standard Model and a naturally light dilaton. Exploiting the full capabilities of these models we identify the parameter space that allows to pass Electroweak Precision Tests with a moderate Kaluza-Klein scale, around 2 TeV. We analyze the coupling of the dilaton with Standard Model (SM) fields in the bulk, and discuss two applications: i) Models with a light dilaton as the first particle beyond the SM pass quite easily all observational tests even with a dilaton lighter than the Higgs. However the possibility of a 125 GeV dilaton as a Higgs impostor is essentially disfavored; ii) We show how to extend the soft wall models to realize a 750 GeV dilaton that could explain the recently reported diphoton excess at the LHC.

Light-front holographic QCD with generic dilaton profile

We generalize the soft-wall and hard-wall models to a light-front holographic QCD model with a generic dilaton profile. The effective potential induced by a higher power dilaton profile is interpreted as a stronger color confinement at long distance, and it gradually evolves to the hard-wall model when the power increases to infinity. As an application, we investigate the exotic meson states recently discovered in experiments in the generic soft-wall model with a higher power dilaton profile, and the results are in agreement with the spectra of the exotic mesons. Our calculation indicates a weaker interaction at short distance and a stronger interaction at large distance for the components in the exotic mesons. The generic dilaton profile deserves further scrutiny for understanding the strong interaction and for applications.

Longitudinal momentum densities in transverse plane for nucleons

We present a study of longitudinal momentum densities ($p^+ \rm densities$) in the transverse impact parameter space for $u$ and $d$ quarks in both unpolarized and transversely polarized nucleons by taking a two dimensional Fourier transform of the gravitational form factors with respect to the momentum transfer in the transverse direction. The gravitational form factors are obtained by the second moments of GPDs. Here we consider the GPDs of two different soft-wall models in AdS/QCD correspondence.