Light-front dynamics and AdS/QCD correspondence: Gravitational form factors of composite hadrons

Abstract

Light-front holography is a remarkable feature of the AdS/CFT correspondence between gravity in AdS space and conformal field theories in physical space-time; it allows string modes $\ensuremath{\Phi}(z)$ in the anti-de Sitter (AdS) fifth dimension to be precisely mapped to the light-front wave functions of hadrons in physical space-time in terms of a specific light-front impact variable $\ensuremath{\zeta}$ which measures the separation of the quark and gluonic constituents within the hadron. This mapping was originally obtained by matching the exact expression for electromagnetic current matrix elements in AdS space with the corresponding exact expression for the current matrix element using light-front theory in physical space-time. In this paper we show that one obtains the identical holographic mapping using matrix elements of the energy-momentum tensor. To prove this, we show that there exists a correspondence between the matrix elements of the energy-momentum tensor of the fundamental hadronic constituents in QCD with the transition amplitudes describing the interaction of string modes in AdS space with an external graviton field which propagates in the AdS interior. The agreement of the results for electromagnetic and gravitational hadronic transition amplitudes provides an important consistency test and verification of holographic mapping from AdS to physical observables defined on the light front.