Holographic pomeron and entropy

Abstract

In dipole-dipole scattering at large rapidity $\ensuremath{\chi}=\mathrm{ln}(s/{s}_{0})$, the induced instanton on the string world sheet carries entropy ${\mathbf{S}}_{k}=2({\ensuremath{\alpha}}_{\mathbf{P}k}\ensuremath{-}1)\ensuremath{\chi}$, with ${\ensuremath{\alpha}}_{\mathbf{P}k}\ensuremath{-}1$ the Pomeron intercept for a dipole source of N-ality $k$. We argue that this entropy is released promptly over a time ${t}_{R}\ensuremath{\approx}({\mathbf{b}}_{\ensuremath{\perp}}/\ensuremath{\chi}{)}^{3}/(4{\ensuremath{\alpha}}^{\ensuremath{'}})$, with ${\ensuremath{\alpha}}^{\ensuremath{'}}/2$ the Pomeron slope and ${\mathbf{b}}_{\ensuremath{\perp}}$ the impact parameter. This stringy entropy may explain the $3/2$ jump in the total charged multiplicities at about ten participants reported over a wide range of collider energies by PHOBOS. We predict the charged multiplicities in $pp$, $pA$ and central $AA$ collisions at LHC.