a b s t r a c tIn this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical space-time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q 2 the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q 2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.

We show how the string amplitude Φ(z) defined on the fifth dimension in AdS5 space can be precisely mapped to the light-front wavefunctions of hadrons in physical spacetime. We find an exact correspondence between the holographic variable z and an impact variable ζ, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schrödinger equations for the bound states of massless quarks and gluons which exactly reproduce the AdS/CFT results and give a realistic description of the light-quark meson and baryon spectrum as well as the form factors for spacelike Q 2 . Only one parameter which sets the mass scale, ΛQCD, is introduced.PACS numbers: 11.15. Tk, 11.25Tq, 12.38Aw, 12.40Yx The correspondence [1] between 10-dimensional string theory defined on AdS 5 × S 5 and conformal Yang-Mills gauge theories in physical 3+1 space-time has led to important insights into the properties of conformal theories at strong coupling. QCD is nearly conformal in the ultraviolet region. It is also a confining gauge theory in the infrared with a mass gap characterized by a scale Λ QCD and a well-defined spectrum of color-singlet hadronic states. Although QCD is not conformal, many aspects of the theory, such as the dimensional scaling of exclusive amplitudes [2], follow if the QCD coupling has an infrared fixed point, allowing one to take conformal symmetry as an initial approximation.The essential principle which leads to AdS/CFT duality is the fact that the group SO(2, 4) of Lorentz and conformal transformations has a mathematical representation on AdS 5 : the isomorphism of the group SO(2,4) of conformal QCD in the limit of massless quarks and vanishing β-function with the isometries of AdS space, x µ → λx µ , z → λz, maps scale transformations into the the holographic coordinate z, the extension of the hadron wavefunction into the fifth dimension. Different values of z determine the scale of the invariant separation between quarks. In particular, the z → 0 boundary corresponds to the Q → ∞, zero separation limit. As shown by Polchinski and Strassler [3], the resulting hadronic theory has the hard behavior and dimensional counting rules [2] expected from a conformal approximation to QCD, rather than the soft behavior characteristic of string theory.Color confinement implies that there is a maximum separation of quarks and a maximum value of z. The cutoff at z 0 = 1/Λ QCD breaks conformal invariance and allows the introduction of the QCD scale. In fact, this holographic model gives a realistic description of the lightquark meson and baryon spectrum [4], including orbital excitations, as well as the meson and baryon form factors for spacelike Q 2 . Remarkably, only one parameter Λ QCD , enters the predictions. Essential features of QCD, its near-conformal behavior at short physical distances plus color confinement at large interquark separation, are incorporated in the model. This approach known as holographic QCD, has been successful in obtaining ...

The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspects of QCD such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter (AdS) space z and a specific light-front impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and which allow the computation of decay constants, form factors and other exclusive scattering amplitudes. Relativistic light-front equations in ordinary space-time are found which reproduce the results obtained using the fifth-dimensional theory. As specific examples we compute the pion coupling constant fπ, the pion charge radius˙r 2 π¸a nd examine the propagation of the electromagnetic current in AdS space, which determines the space and time-like behavior of the pion form factor and the pole of the ρ meson.