Light-Front Quantization and AdS/QCD: An overview

Abstract

We give an overview of the light front holographic approach to strongly coupled QCD, whereby a confining gauge theory quantized on the light front is mapped to a higher-dimensional anti de Sitter (AdS) space incorporating the AdS/CFT correspondence as a useful guide. One can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable ζ, which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background which encodes salient properties of the QCD dual theory, such as the ultraviolet conformal limit at the AdS boundary at z → 0, as well as modifications of the background geometry in the large z infrared region to describe confinement. In the semiclassical approximation both approaches are equivalent. This allows us to identify the holographic variable z in AdS space with the impact variable ζ. 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, in light front holography the internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.