We investigate nonlinear extensions of the holographic soft wall model proposed by Karch, Katz, Son and Stephanov \cite{Karch:2006pv} with a positive quadratic dilaton. We consider a Higgs potential for the tachyonic field that brings a more natural realisation of chiral symmetry breaking in the infrared regime. Utilising the AdS/CFT dictionary and holographic renormalisation 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 Schrödinger 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 behaviour for the decay constants as the quark mass increases. We also investigate the effect of a 5d 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.
In the context of theories with a first order phase transition, we propose a general covariant description of coexisting phases separated by domain walls using an additional order parameter-like degree of freedom. In the case of a holographic Witten model with a confining and deconfined phase, the resulting model extends hydrodynamics and has a simple formulation in terms of a spacetime action with corresponding expressions for the energy-momentum tensor. The proposed description leads to simple analytic profiles of domain walls, including expressions for surface tension density, which agree n…
We study a realization of light dilatons by considering Conformal Field Theories deformed by a nearly marginal operator ${\cal O}$. This is discussed in the holographic setup consisting of Renormalization Group flows that end on a soft wall. We obtain a mass formula for the dilaton as an average along the flow. Finally we discuss the holographic method to compute the condensate $\langle {\cal O} \rangle$.
We study confinement-deconfinement phase transition in a holographic soft-wall QCD model. By solving the Einstein-Maxwell-scalar system analytically, we obtain the phase structure of the black hole backgrounds. We then impose probe open strings in such background to investigate the confinement-deconfinement phase transition from different open string configurations under various temperatures and chemical potentials. Furthermore, we study the Wilson loop by calculating the minimal surface of the probing open string world-sheet and obtain the Cornell potential in confinement phase analytically.
We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model and interpret our result as the heavy quarks system by comparing the recent lattice QCD simulation. We finally obtain the equations of state in our model.
We apply the soft wall holographic model from hadron physics to a description of the high-$T_c$ superconductivity. In comparison with the existing bottom-up holographic superconductors, the proposed approach is more phenomenological. On the other hand, it is much simpler and has more freedom for fitting the conductivity properties of the real high-$T_c$ materials. We demonstrate some examples of emerging models and discuss a possible origin of the approach.
In this paper we describe qualitatively some aspects of the holographic QCD. Inspired by a successfull 4D description, we try to separate the Confinement and the Chiral Symmetry Breaking dynamics. We also discuss the realization of the baryons as skyrmions in Soft Wall Holographic QCD, and the issue of the Vector Meson Dominance.
We derive a light-front Schrodinger-type equation of motion for the quark-antiquark wave function of heavy quarkonia imposing constraints from 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 phenomenologica…
We propose a modification of soft-wall holographic model that in combination with the light-front holographic QCD leads to a broad hydrogen-like degeneracy of the same sort as the degeneracy observed experimentally in the spectrum of light mesons.
We use the no-wall holographic approach (a relative of the soft-wall one) to construct a universal description of vector mesons with arbitrary quark masses. The proposed model predicts a specific dependence of the parameters of radial Regge trajectories on the quark masses in a reasonable agreement with the meson phenomenology and some theoretical expectations.
We study the mass spectrum and decay constants of light and heavy mesons in a soft-wall holographic approach, using the correspondence of string theory in Anti-de Sitter space and conformal field theory in physical space-time.
We propose a new type of bottom-up holographic model describing the Regge like spectrum of mesons. This type of spectrum emerges due to condensation of a scalar field in the bulk anti-de Sitter space. The gauge invariance of the action describing the vector mesons requires that the bulk scalar field must correspond to an operator of canonical dimension two. This is not necessary for the description of the scalar sector where the generation of the mass spectrum can be directly related to the formation of gluon condensate in QCD. It is also demonstrated that such an explicit introduction of loca…
We discuss the vertex function of two vector and one axial-vector operators in the soft-wall holographic model of QCD. When one of the two vector currents represents an on-shell soft photon, such a vertex is described by two structure functions $w_L$ and $w_T$, which are usually calculated through triangular loop diagrams. We evaluate these functions in the soft-wall model of holographic QCD (HQCD) and compare the outcome to the QCD findings.
We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field.
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 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 take place in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up ho…
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 r…
We study the vertex function of two vector and one axial-vector operators in the soft-wall holographic model of QCD. In particular, we discuss the possible relation, introduced by Son and Yamamoto, between the structure function $w_T$ describing such a vertex when one of the two vector currents represents an on-shell soft photon and the the two-point $Π_\perp^{VV}-Π_\perp^{AA}$ correlation function.
In a hard-wall model of holographic QCD, we find that nonlinear boundary dynamics are required in order to maintain the correct pattern of explicit and spontaneous chiral symmetry breaking beyond leading order in the pion fields. With the help of a field redefinition, we relate the requisite nonlinear boundary conditions to a standard Sturm-Liouville system. Observables insensitive to the chiral limit receive only small corrections in the improved description, and classical calculations in the hard-wall model remain surprisingly accurate.
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 …
We study the phenomenology of the recently proposed modified version of the Soft-Wall model of holographic QCD with a negative dilaton profile. We investigate vector and scalar mesons, evaluating mass spectra, decay constants and two-point correlation functions. We then study chiral symmetry breaking and compute the coupling of a scalar meson with two pseudoscalars. Finally, we compare the results with the ones found in the literature in the positive-dilaton case.
Recently, it has been suggested that large-Nc orbifold equivalences may be applicable to certain theories with chemical potentials, including QCD, in certain portions of their phase diagram. When valid, such an equivalence offers the possibility of relating large-Nc QCD at non-zero baryon chemical potential, a theory with a complex fermion determinant, to a related theory whose fermion determinant is real and positive. In this paper, we provide a test of this large Nc equivalence using a holographic realization of a supersymmetric theory with baryon chemical potential and a related theory with…
Mesons and baryons are considered in soft-wall holographic approach based on the correspondence of string theory in AdS space and conformal field theory in physical space-time. The model generates Regge trajectories linear in n and J (L) for the hadronic mass spectrum. Results obtained for heavy-light meson masses and decay constants are consistent with predictions of HQET. In the baryon sector applications to the nucleon electromagnetic form factors and generalized parton distributions are discussed.
We reassess employing the holographic technique to the description of 4D minimal composite Higgs model with $SO(5)\to SO(4)$ global symmetry breaking pattern. The particular 5D bottom-up holographic treatment is inspired by previous work in the context of QCD and it allows to study spin one and spin zero resonances. The resulting spectrum consists of the states transforming under the unbroken $SO(4)$ subgroup and those with quantum numbers in the $SO(5)/SO(4)$ coset. The spin one states are arranged in linear radial trajectories, and the states from the broken subgroup are generally heavier. T…
We study the thermodynamical phase structures of holographic QCD with nontrivial topologically charged domain-wall/membranes which are originally related to the multiple $θ$-vacua in the large $N_c$ limit. We realize the topologically charged membranes as the holographic D6-brane fluxes in the Sakai-Sugimoto model. The D6-brane fluxes couple to the probe D8-anti-D8 via Chern-Simon term, and act as the source for the baryonic current density of QCD. We find rich phase structures of the dual meson system by varying asymptotic separation of D8 and anti-D8. Especially, there can be a thermodynamic…
We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field. We show that in the case of the bound-state problem (hadronic mass spectrum) two versions of the model with a positive and negative dilaton profile are equivalent to each other by a special transformation of the bulk field. We also comment on recent works which discuss the dilaton s…
The holographic methods inspired by the gauge/gravity correspondence from string theory have been actively applied to the hadron spectroscopy in the last eleven years. Within the phenomenological bottom-up approach, the linear Regge-like trajectories for light mesons are naturally reproduced in the so-called "Soft-wall" holographic models. I will give a very short review of the underlying ideas and technical aspects related to the meson spectroscopy. A generalization of soft-wall description of Regge trajectories to arbitrary intercept is proposed. The problem of incorporation of the chiral sy…
We use holography to study Conformal Phase Transitions, which are believed to be realized in four dimensional QCD and play an important role in walking technicolor models of electroweak symmetry breaking. At strong coupling they can be modeled by the non-linear dynamics of a tachyonic scalar field with mass close to the Breitenlohner-Freedman bound in anti de Sitter spacetime. Taking the action for this field to have a Tachyon-Dirac-Born-Infeld form gives rise to models that resemble hard and soft wall AdS/QCD, with a dynamically generated wall. For hard wall models, the highly excited spectru…
We study the scalar glueball and vector meson spectral functions in a hot and dense medium by means of the soft-wall holographic model of QCD. Finite temperature and density effects are implemented through the AdS/RN metric. We analyse the behaviour of the hadron masses and widths in the $(T,μ)$ plane, and compare our results with the experimental ones and with other theoretical determinations.
The singlet pseudoscalar sector of light mesons is investigated in the soft-wall model, a bottom-up approach to the AdS/QCD correspondence. The $η^\prime$ 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.
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. Motiv…
Using a five-dimensional warped model including a scalar potential with an exponential behavior in the infrared, and strong back-reaction over the metric, we study the electroweak phase transition, and explore parameter regions that were previously inaccessible. The model exhibits gravitational waves and predicts a stochastic gravitational wave background observable, both at the Laser Interferometer Space Antenna and at the Einstein Telescope. Moreover, concerning the collider signatures predictions, the radion evades current constraints but may show up in future LHC runs.
We calculate the symmetry energy of the nuclear matter by using the bottom-up approach, so called hard wall model. To consider the nuclear matter, we introduce the isospin for u- and d-quarks. We find that in the hard wall model, the symmetry energy of the nuclear matter is proportional to the square of nucleon density. We also study the symmetry energy of the quark matter in the deconfining phase. Finally, we investigate the effect of the symmetry energy on the Hawking-Page transition and show that at the given quark density, the Hawking-Page transition temperature decreases due to the symmet…
I consider the three-point function of two vector and one axial-vector currents. In the kinematic configuration in which one of the two vector currents corresponds to an on-shell soft photon, such a vertex is described in QCD by two functions, $w_L$ and $w_T$. After reviewing the properties of these functions in QCD, I describe the result obtained using the soft-wall holographic model of QCD with the addition of the Chern-Simons term and I compare it with the QCD outcome. I also discuss a relation, proposed by Son and Yamamoto, that connects $w_L$ and $w_T$ to the two-point functions $Π_{VV}$ …
We derive and systematically analyze scalar glueball correlation functions in both the hard-wall and dilaton soft-wall approximations to holographic QCD. The dynamical content of the holographic correlators is uncovered by examining their spectral density and by relating them to the operator product expansion, a dilatational low-energy theorem and a recently suggested two-dimensional power correction associated with the short-distance behavior of the heavy-quark potential. This approach provides holographic estimates for the three lowest-dimensional gluon condensates or alternatively their Wil…
We consider the vertex function of two vector and one axial-vector currents using the soft-wall holographic model of QCD with the Chern-Simons term. Two structure functions $w_L$ and $w_T$ describe such a vertex in the special case in which one of the two vector currents corresponds to an on-shell soft photon. We briefly review the QCD results for these functions, obtained from triangular loop diagrams with quarks having mass $m_q=0$ or $m_q \neq 0$, we compute $w_L$ and $w_T$ in the soft-wall model and compare the outcome to the QCD findings. We also calculate and discuss the two-point $Π_{VV…
Holographic soft-wall model is successful in the phenomenology of hadrons. Here with the use of generalized parton distributions (GPDs) obtained from AdS/QCD, perturbative effects are entered into the formalism. Perturbations are incorporated in the formalism through the evolution of GPDs according to the DGLAP like equations. Evolved proton GPDs are compared with a phenomenological model to show that we can get good improvements of the holographic model. It seems that combining the holographic soft-wall model with perturbative effects to some extent, gives the correct physics of GPDs.
Wave functions and form factors of vector mesons are investigated in the holographic dual model of QCD with a smooth oscillator-like wall. We introduce wave functions conjugate to solutions of the 5D equation of motion and develop a formalism based on these wave functions, which are very similar to those of a quantum-mechanical oscillator. For the lowest bound state (rho-meson), we show that, in this model, the basic elastic form factor exhibits the perfect vector meson dominance, i.e., it is given by the rho-pole contribution alone. The electric radius of the rho-meson is calculated, <r^2_rho…
In this investigation an holographic description of the deconfined phase transition of scalar and tensor glueballs is presented within the so called hard-wall model. The spectra of these bound states of gluons have been calculated from the linearized Einstein equations for a graviton propagating from a thermal $AdS_5$ space to an AdS Black-Hole. In this framework, the deconfined phase is reached via a two steps mechanism. We propose that the transition between the AdS thermal sector to the BH is described via a first order phase transition, with discontinuous masses at the critical temperature…
We study models of gauge mediation with strongly coupled hidden sectors, employing a hard wall background as an holographic dual description. The structure of the soft spectrum depends crucially on the boundary conditions one imposes on bulk fields at the IR wall. Generically, vector and fermion correlators have poles at zero momentum, leading to gauge mediation by massive vector messengers and/or generating Dirac gaugino masses. Instead, non-generic choices of boundary conditions let one cover all of GGM parameter space. Enriching the background with R-symmetry breaking scalars, the SSM soft …
We argue that deconfinement in AdS/QCD models occurs via a first order Hawking-Page type phase transition between a low temperature thermal AdS space and a high temperature black hole. Such a result is consistent with the expected temperature independence, to leading order in 1/N_c, of the meson spectrum and spatial Wilson loops below the deconfinement temperature. As a byproduct, we obtain model dependent deconfinement temperatures T_c in the hard and soft wall models of AdS/QCD. Our result for T_c in the soft wall model is close to a recent lattice prediction.
In this paper, minimal coupling constants of meson-$Δ$ baryon and meson-nucleon to $Δ$ baryon transition have been investigated in the AdS/QCD soft-wall model at finite temperature limits. Initially, the right and left profile functions of $Δ$ baryons have been calculated using the Rarita-Schwinger field in this model. After this, coupling constants have been written by taking into account the profile functions of thermal hadrons according to the zero-temperature case. Then, the temperature dependence graphs are plotted for strong couplings $g_{ρΔΔ}(T)$, $g_{a_{1} ΔΔ}(T)$ and $g_{ρN Δ}(T)$. As…
With proper profiles of the scalar potential and the dilaton field, for the first time, the spontaneous chiral symmetry breaking in the vacuum and its restoration at finite temperature are correctly realized in the holographic QCD framework. In the chiral limit, a nonzero chiral condensate develops in the vacuum and decreases with temperature, and the phase transition is of 2nd order for two-flavor case and of 1st order for three-flavor case. In the case of explicit chiral symmetry breaking, in two-flavor case, the 2nd order phase transition turns to crossover with any nonzero current quark ma…
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 we…
We first study Z(N) walls in a deconfined phase of Witten's D4-brane background of pure SU(N) Yang-Mills theory, motivated by a recent work in the case of N=4 SYM. Similarly to it, we propose that for a large wall charge k ~ N, it is described by k D2-branes blown up into a NS5-brane wrapping S^3 inside S^4 via Myers effect, and we calculate the tension by suitable U-duality. We find a precise Casimir scaling for the tension formula. We then study the fate of Z(N)-vacua in a presence of fundamental flavors in quenched approximation via gauge/gravity correspondence. In the case of D3/D7 system …
Using a holographic dual model of QCD, we compute the pion electromagnetic form factor F_pi(Q^2) in the spacelike momentum transfer region, as well as pion couplings to vector mesons g_rho^(n) pi pi. Spontaneous and explicit chiral symmetry breaking are intrinsic features of this particular holographic model. We consider variants with both ``hard-wall'' and ``soft-wall'' infrared cutoffs, and find that the F_pi(Q^2) data tend to lie closer to the hard-wall model predictions, although both are too shallow for large Q^2. By allowing the parameters of the soft-wall model (originally fixed by obse…
We derive the general 5-dimension metric structure of the $Dp-Dq$ system in type II superstring theory, and demonstrate the physical meaning of the parameters characterizing the 5-dimension metric structure of the \textit{holographic} QCD model by relating them to the parameters describing Regge trajectories. By matching the spectra of vector mesons $ρ_1$ with deformed $Dp-Dq$ soft-wall model, we find that the spectra of vector mesons $ρ_1$ can be described very well in the soft-wall $D3-Dq$ model, i.e, $AdS_5$ soft-wall model. We then investigate how well the $AdS_5$ soft-wall model can descr…
