Hadrons in AdS/QCD Models

International Journal of Modern Physics E, 2007

An approximate holographic dual of QCD is constructed and shown to reproduce the empirical linear trajectories of universal slope on which the square masses of radially and orbitally excited hadrons join. Conformal symmetry breaking and other IR effects are described exclusively by deformations of the anti-de Sitter background metric. The predictions for the light hadron spectrum include new relations between ground state masses and trajectory slopes and are in good overall agreement with experimental data.

2010

We find a correspondence between semiclassical QCD quantized on the lightfront and a dual gravity model in anti-de Sitter (AdS) space, thus providing an initial approximation to QCD in its strongly coupled regime. This correspondence-light-front holography-leads to a light-front Hamiltonian and relativistic bound-state wave equations that are functions of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within hadrons at equal light-front time. The eigenvalues of the resulting light-front Schrödinger and Dirac equations are consistent with the observed light meson and baryon spectrum, and the eigenmodes provide the light-front wavefunctions, the probability amplitudes describing the dynamics of the hadronic constituents. The light-front equations of motion, which are dual to an effective classical gravity theory, possess remarkable algebraic and integrability properties which are dictated by the underlying conformal properties of the theory. We extend the algebraic construction to include a confining potential while preserving the integrability of the mesonic and baryonic bound-state equations.

Physical Review D, 2009

We present an holographical soft wall model which is able to reproduce not only Regge spectra for hadrons with arbitrary integer spin, but also with spin 1/2 and 3/2, and with an arbitrary number of constituents. The model includes the anomalous dimension of operators than create hadrons, together with a dilaton, whose form is suggested by Einstein equations and the AdS metric used.

We compute the spectrum of light hadrons in a holographic dual of QCD defined on AdS5 × S 5 which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale ΛQCD, is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of delta to nucleon trajectories is determined by the ratio of zeros of Bessel functions.

Nuclear Physics B - Proceedings Supplements, 2010

We show that a Dynamical AdS/QCD model is able to reproduce the linear Regge trajectories for the light-flavor sector of mesons with high spin and also for the scalar and pseudoscalar ones. In addition the model has confinement by the Wilson loop criteria and a mass gap. We also calculate the decay amplitude of scalars into two pion in good agreement to the available experimental data.

Nucleation and Atmospheric Aerosols, 2006

The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. We have recently shown how a holographic model based on a truncated AdS space can be used to obtain the hadronic spectrum of light qq, qqq and gg bound states. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state, including orbital angular momentum excitations. The predicted mass spectrum is linear M ∝ L at high orbital angular momentum, in contrast to the quadratic dependence M 2 ∝ L found in the description of spinning strings. Since only one parameter, the QCD scale Λ QCD , is introduced, the agreement with the pattern of physical states is remarkable. In particular, the ratio of ∆ to nucleon trajectories is determined by the ratio of zeros of Bessel functions. The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. One can also use the extended AdS/CFT space-time theory to obtain a model for hadronic light-front wavefunctions, thus providing a relativistic description of hadrons in QCD at the amplitude level. The model wavefunctions display confinement at large inter-quark separation and conformal symmetry at short distances. In particular, the scaling and conformal properties of the LFWFs at high relative momenta agree with perturbative QCD. These AdS/CFT model wavefunctions could be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. We also show how hadron form factors in both the space-like and time-like regions can be predicted.

We consider the particle spectrum and event shapes in large N gauge theories in different regimes of the short-distance 't Hooft coupling, lambda. The mesons in the small lambda limit should have a Regge spectrum in order to agree with perturbation theory, while generically the large lambda theories with gravity duals produce spectra reminiscent of KK modes. We argue that these KK-like states are qualitatively different from QCD modes: they are deeply bound states which are sensitive to short distance interactions rather than the flux tube-like states expected in asymptotically free, confining gauge theories. In addition, we also find that the characteristic event shapes for the large lambda theories with gravity duals are close to spherical, very different from QCD-like (small lambda, small N) and Nambu-Goto-like (small lambda, large N) theories which have jets. This observation is in agreement with the conjecture of Strassler on event shapes in large 't Hooft coupling theories, which was recently proved by Hofman and Maldacena for the conformal case. This conclusion does not change even when considering soft-wall backgrounds in the gravity dual. The picture that emerges is the following: theories with small and large lambda are qualitatively different, while theories with small and large N are qualitatively similar. Thus it seems that it is the relative smallness of the 't Hooft coupling in QCD that prevents a reliable AdS/QCD correspondence from emerging, and that reproducing characteristic QCD-like behavior will require genuine stringy dynamics to be incorporated into any putative dual theory.

Int J Mod Phys D, 2010

We show that a dynamical AdS/QCD model is able to reproduce the linear Regge trajectories for the light-flavor sector of mesons with high spin and also for the scalar and pseudo-scalar ones. In addition the model has confinement by the Wilson loop criteria and a mass gap. We also calculate the decay amplitude of scalars into two pion with a good agreement with the available experimental data.

The European Physical Journal A, 2016

The real parts of the complex squared energies defined by the resonance poles of the transfer matrix of the Pöschl-Teller barrier, are shown to equal the squared energies of the levels bound within the trigonometric Scarf well potential. By transforming these potentials into parts of the Laplacians describing free quantum motions on the mutually orthogonal open time-like hyperbolic-, and closed space-like spherical geodesics on the conformally invariant de Sitter space time, dS4, the conformal symmetries of these interactions are revealed. On dS4 the potentials under consideration naturally relate to interactions within colorless two-body systems and to cusped Wilson loops. In effect, with the aid of the dS4 space-time as unifying geometry, a conformal symmetry based bijective correspondence (duality) between bound and resonant meson spectra is established at the quantum mechanics level and related to confinement understood as color charge neutrality. The correspondence allows to link the interpretation of mesons as resonance poles of a scattering matrix with their complementary description as states bound by an instantaneous quark interaction and to introduce a conformal symmetry based classification scheme of mesons. As examples representative of such a duality we organize in good agreement with data 71 of the reported light flavor mesons with masses below ∼ 2350 MeV into four-conformal families of particles placed on linear f0, π, η, and a0 resonance trajectories, plotted on the ℓ/M plane. Upon extending the sec 2 χ by a properly constructed conformal color dipole potential, shaped after a tangent function, we predict the masses of 12 "missing" mesons. We furthermore notice that the f0 and π trajectories can be viewed as chiral partners, same as the η and a0 trajectories, an indication that chiral symmetry for mesons is likely to be realized in terms of parity doubled conformal multiplets rather than, as usually assumed, only in terms of parity doubled single SO(3) states. We attribute the striking measured meson degeneracies to conformal symmetry dynamics within color neutral two-body systems, and conclude on the usefulness of the de Sitter space-time dS4 as a tool for modelling strong interactions, on the one side, and on the relevance of hyperbolic and trigonometric potentials in constituent quark models of hadrons, on the other.

Proceedings of Light Cone 2010: Relativistic Hadronic and Particle Physics — PoS(LC2010)

We find a correspondence between semiclassical gauge theories quantized on the light-front and a dual gravity model in anti-de Sitter (AdS) space, thus providing an initial approximation to QCD in its strongly coupled regime. This correspondence-light-front holography-leads to a light-front Hamiltonian and relativistic bound-state wave equations in terms of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. Light-front holography also allows a precise mapping of transition amplitudes from AdS to physical space-time. In contrast with the usual AdS/QCD framework, the internal structure of hadrons is explicitly introduced in the gauge/gravity correspondence and the angular momentum of the constituents plays a key role. We also discuss how to introduce higher Fock-states in the correspondence as well as their relevance for describing the detailed structure of space and time-like form factors.