Deep inelastic and dipole scattering on finite length hot $\mathcal{N}=4$ SYM matter

TL;DR

This paper investigates deep inelastic scattering and dipole interactions with finite length hot $ ext{AdS}_5$-Schwarzschild $ ext{N}=4$ SYM matter, revealing a saturation scale and analyzing operator product expansion and string dynamics.

Contribution

It introduces a saturation momentum scale for scattering on finite length hot $ ext{N}=4$ SYM matter and analyzes the operator product expansion and string behavior in this context.

Findings

Saturation momentum scale $Q_s^2 o LT^3/x$ identified.

OPE series is non-Borel summable for infinite matter, but Borel summable for finite matter.

String dynamics show induced motion and potential breaking in hot matter, constrained by classical approximation.

Abstract

Deep inelastic scattering of $\mathcal{R}$-currents and the scattering of a small dipole on finite length hot $\mathcal{N}=4$ SYM matter are discussed. In each case we find the scale when scattering becomes strong is determined by a saturation momentum $Q^2_s \sim LT^3/x$ where $L$ is the length of the matter. For $\mathcal{R}$-currents we analyze the operator product expansion. For infinite length matter the series generated by the OPE is not Borel summable but we are able to determine the exponential part of the tunneling amplitude determining $F_2$ when $\frac{Q^2}{Q^2_s}\gg 1$ from the position of the singularity closest to the origin on the real axis of the Borel plane. In finite length matter the OPE series is not convergent but it is Borel summable. When a small dipole, and the string connecting the ends of the dipole, pass through hot matter there is an induced motion of the string in the $5^{th}$ dimension. When $T^4 L \cosh \eta$, with the $\eta$ the rapidity of the string, is large enough the string would normally break into several parts after leaving the medium, however, this cannot happen in the classical approximation in which we work.