Shockwaves and deep inelastic scattering within the gauge/gravity duality

Abstract

Within the gauge/gravity correspondence, we discuss the general formulation of the shockwave metric which is dual to a 'nucleus' described by the strongly-coupled N=4 SYM theory in the limit where the number of colors Nc is arbitrarily large. We emphasize that the 'nucleus' must possess Nc^2 degrees of freedom per unit volume, so like a finite-temperature plasma, in order for a supergravity description to exist. We critically reassess previous proposals for introducing transverse inhomogeneity in the shockwave and formulate a new proposal in that sense, which involves no external source but requires the introduction of an 'infrared' cutoff which mimics confinement. This cutoff however plays no role when the shockwave is probed by a highly virtual projectile, so like in deep inelastic scattering. We consider two such projectiles, the dilaton and the R-current, and compute the respective structure functions including unitarity corrections. We find that there are no leading-twist contributions to the structure functions at high virtuality, meaning that there are no point-like constituents in the strongly coupled 'nucleus'. In the black-disk regime at low virtuality, the structure functions are suggestive of parton saturation with occupation numbers of order one. The saturation momentum Qs grows with the energy like Qs^2 ~ 1/x (with x the Bjorken variable), which is the hallmark of graviton exchanges and is also necessary for the fulfillment of the energy-momentum sum rules.