Light-Front Holographic QCD and Emerging Confinement

Abstract

In 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 gives a precise interpretation of holographic variables and quantities in AdS 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.

Figures (17)

• Figure 1: An effective light-front theory for QCD endowed with an $SO(2,1)$ algebraic structure follows from the one-dimensional semiclassical approximation to light-front dynamics in physical space-time, higher dimensional gravity in AdS$_5$ space and the extension of conformal quantum mechanics to light-front dynamics. The result is a relativistic light-front quantum mechanical wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The emergence of a mass scale and the effective confining potential has its origins in the isomorphism of the one-dimensional conformal group ${\it Conf}\!\left(R^1\right)$ with the group $SO(2,1)$, which is also the isometry group of AdS$_2$.
• Figure 2: Dirac forms of relativistic dynamics: (a) the instant form, (b) the front form and (c) the point form. The initial surfaces are defined respectively by $x^0 = 0, \, x^0 + x^3 = 0$ and $x^2 = \kappa^2 >0, \, x^0 >0.$
• Figure 3: Overall and relative partonic variables in a hadronic bound state.
• Figure 4: Relative $q-\bar{q}$ variables in impact space for a pion bound state.
• Figure 5: $\tilde{g}_{00}(z)/ R$ for a positive dilaton profile $\tilde{\varphi}(z) = \lambda z^2 / 3$.